arXiv subjects
Publications and source records attributed to Punam Gupta.
In this paper, we study Clairaut generic Riemannian map from a nearly Kahler manifold to a Riemannian manifold. Further, we obtain a condition for a Clairaut generic Riemannian map to be a totally geodesic foliation on the total manifold. Lastly, we give non-trivial examples of such Riemannian maps.
In this paper, we investigate the transverse geometry of trans-Sasakian manifolds and present several significant findings. We analyze the Levi-Civita connection associated with the metric on the product manifold of two trans-Sasakian manifolds. We outline the conditions under which the complex structure is harmonic on the product manifold. Notably, we also offer valuable insights into the harmonicity of the complex structure within the context of astheno- Kahler manifolds.
In this paper, we investigate the DDVV-type inequality for Riemannian maps from quaternionic space forms to Riemannian manifolds. We also discuss the equality case of the derived inequality with application.
This paper focuses on deriving several curvature inequalities involving the Ricci and scalar curvatures of the horizontal and vertical distributions in anti-invariant Riemannian submersions from quaternionic space forms onto Riemannian manifolds. In addition, a Ricci curvature inequality for anti-invariant Riemannian submersions is established. The equality cases for all derived inequalities are also examined.
We investigate the conditions under which astheno-K\"ahler structures can be identified on the product of two compact trans-Sasakian manifolds of dimensions greater than 2.
We explore h-conformal semi-invariant submersions and almost h-conformal semi-invariant submersions originating from quaternionic K\"ahler manifolds to Riemannian manifolds. Our investigation focuses on the geometric characteristics of these submersions, including the integrability of distributions and the geometry of foliations. Additionally, we establish the necessary and sufficient conditions for such submersions to be totally geodesic. We also examine the equivalent conditions for the total manifold of the submersion to be twisted product manifold. Finally, we present a series of examples illustrating quaternionic K\"ahler manifolds and h-conformal semi-invariant submersions from quaternionic K\"ahler manifolds to Riemannian manifolds.
This survey explores a range of classical findings and recent developments related to our understanding of astheno-K\"ahler manifolds. Furthermore, we provide various examples of astheno-K\"ahler manifolds and analyze the challenges associated with their existence.
The present paper deals with the characterization of a new submersion named semi-invariant conformal $ζ^{\perp }$-Riemannian submersion from almost contact metric manifolds onto Riemannian manifolds which is the generalization of some known submersions on Riemannian manifolds. We give important and adequate conditions for such submersions to be totally geodesic and harmonic. Also, few examples are examined for such submersions endowed with horizontal Reeb vector field.
The purpose of the present paper to study a second order symmetric parallel tensor in generalized f.pk-space form. Second order symmetric parallel tensor in f.pk-space form is combination of the associated metric tensor and $1$-forms of structure vector fields. We prove that there does not exist second order skew-symmetric parallel tensor in f.pk-space form. We also deduce that there is no parallel hypersurface in a generalized f.pk-space form but there is semi-parallel hypersurfaces in a generalized f.pk-space form.
The aim of this paper is to extend the notion of all known quasi-Einstein manifolds like generalized quasi-Einstein, mixed generalized quasi-Einstein manifold, pseudo generalized quasi-Einstein manifold and many more and name it comprehensive quasi Einstein manifold C(QE)$_{n}$. We investigate some geometric and physical properties of the comprehensive quasi Einstein manifolds C(QE)$_{n}$ under certain conditions. We study the conformal and conharmonic mappings between C(QE)$_{n}$ manifolds. Then we examine the C(QE)$_{n}$ with harmonic Weyl tensor. We investigate geometric and physical properties of the comprehensive quasi Einstein manifolds C(QE)$_{n}$ under certain conditions. We define the manifold of comprehensive quasi-constant curvature and proved that conformally flat C(QE)$_{n}$ is manifold of comprehensive quasi-constant curvature and vice versa. We study the general two viscous fluid spacetime C(QE)$_{4}$ and find out some important consequences about C(QE)$_{4}$. We study C(QE)$_{n}$ with vanishing space matter tensor. Finally, we prove the existence of such manifolds by constructing non-trivial example.
The aim of this paper is to introduce a cosymplectic analouge of conformal connection in a cosymplectic manifold and proved that if cosymplectic manifold M admits a cosymplectic conformal connection which is of zero curvature, then the Bochner curvature tensor of M vanishes.
In the present paper, we investigate geometric properties of Clairaut anti-invariant submersions whose total space is a nearly Kaehler manifold. We obtain condition for Clairaut anti-invariant submersion to be a totally geodesic map and also study Clairaut anti-invariant submersions with totally umbilical fibers. In the last, we introduce illustrative example.
In this paper, we prove that the deformed Riemannian extension of any affine Szabó manifold is a Szabó pseudo-Riemannian metric and vice-versa. We proved that the Ricci tensor of an affine surface is skew-symmetric and nonzero everywhere if and only if the affine surface is Szabó. We also find the necessary and sufficient condition for the affine Szabó surface to be recurrent. We prove that for an affine Szabó recurrent surface the recurrence covector of a recurrence tensor is not locally a gradient.
In this paper, we study the doubly warped product manifolds with semisymmetric metric connection. We derive the curvatures formulas for doubly warped product manifold with semi-symmetric metric connection in terms of curvatures of components of doubly warped product manifolds. We also prove the necessary and sufficient condition for a doubly warped product manifold to be a warped product manifold. We obtain some results for Einstein doubly warped product manifold and Einstein-like doubly warped product manifold of class A with respect to a semi-symmetric metric connection.
The purpose of the present paper is to study the globally and locally $φ$-${\cal T}$-symmetric $\left( \varepsilon \right) $-para Sasakian manifold in dimension $3$. The globally $φ$-$ {\cal T}$-symmetric $3$-dimensional $\left( \varepsilon \right) $-para Sasakian manifold is either Einstein manifold or has a constant scalar curvature. The necessary and sufficient condition for Einstein manifold to be globally $φ$-${\cal T}$ -symmetric is given. A $3$-dimensional $% \left( \varepsilon \right) $ -para Sasakian manifold is locally $φ$-$ {\cal T}$-symmetric if and only if the scalar curvature $r$ is constant. A $3 $-dimensional $\left( \varepsilon \right) $-para Sasakian manifold with $% η$-parallel Ricci tensor is locally $φ$-${\cal T}$-symmetric. In the last, an example of $3$-dimensional locally $φ$-${\cal T}$-symmetric $\left( \varepsilon \right) $-para Sasakian manifold is given.
Definition of $({\cal T}_{a},{\cal T}_{b})$-pseudosymmetric semi-Riemannian manifold is given. $({\cal T}_{a},{\cal T}_{b})$-pseudosy mmetric $(N(k),ξ)$-semi-Riemannian manifolds are classified. Some results for ${\cal T}_{a}$-pseudosymmetric $(N(k),ξ)$-semi-Riemannian manifolds are obtained. $({\cal T}_{a},{\cal T}_{b},S^{\ell})$-pseudosymmetric semi-Riemannian manifolds are defined. $({\cal T}_{a},{\cal T}_{b},S^{\ell})$-pseudosymmetric $(N(k),ξ)$-semi-Riemannian manifolds are classified. Some results for $(R,{\cal T}_{a},S^{\ell})$-pseudosymmetric $(N(k),ξ)$-semi-Riemannian manifolds are obtained. In particular, some results for $(R,{\cal T}_{a},S)$-pseudosymmetric $(N(k),ξ)$-semi-Riemannian manifolds are also obtained. After that, the definition of $({\cal T}_{a},S_{{\cal T}_{b}})$-pseudosymmetric semi-Riemannian manifold is given. $({\cal T}_{a},S_{{\cal T}_{b}})$-pseudosymmetric $(N(k),ξ)$-semi-Riemannian manifolds are classified. It is proved that a $(R,S_{{\cal T}_{a}})$-pseudosymmetric $(N(k),ξ)$-semi-Riemannian manifold is either Einstein or $L=k$ under an algebraic condition. Some results for $({\cal T}_{a},S)$-pseudosymmetric $(N(k),ξ)$-semi-Riemannian manifolds are also obtained. In last, $({\cal T}_{a},S_{{\cal T}_{b}},S^{\ell})$-pseudosymmetric semi-Riemannian manifolds are defined and $({\cal T}_{a},S_{{\cal T}_{b}},S^{\ell})$ -pseudosymmetric $(N(k),ξ)$-semi-Riemannian manifolds are classified.
$(N(k),ξ)$-semi-Riemannian manifolds are defined. Examples and properties of $(N(k),ξ)$-semi-Riemannian manifolds are given. Some relations involving ${\cal T}_{a}$-curvature tensor in $(N(k),ξ)$-semi-Riemannian manifolds are proved. $ξ$-${\cal T}_{a}$-flat $(N(k),ξ)$-semi-Riemannian manifolds are defined. It is proved that if $M$ is an $n$-dimensional $ξ$-${\cal T}_{a}$-flat $(N(k),ξ)$-semi-Riemannian manifold, then it is $η$-Einstein under an algebraic condition. We prove that a semi-Riemannian manifold, which is $T$-recurrent or $T$-symmetric, is always $T$-semisymmetric, where $T$ is any tensor of type $(1,3)$. $({\cal T}_{a}, {\cal T}_{b}) $-semisymmetric semi-Riemannian manifold is defined and studied. The results for ${\cal T}_{a}$-semisymmetric, ${\cal T}_{a}$-symmetric, ${\cal T}_{a}$-recurrent $(N(k),ξ)$-semi-Riemannian manifolds are obtained. The definition of $({\cal T}_{a},S_{{\cal T}_{b}})$-semisymmetric semi-Riemannian manifold is given. $({\cal T}_{a},S_{{\cal T}_{b}})$-semisymmetric $(N(k),ξ)$-semi-Riemannian manifolds are classified. Some results for ${\cal T}_{a}$-Ricci-semisymmetric $(N(k),ξ)$-semi-Riemannian manifolds are obtained.
We find the index of $\widetilde{\nabla}$-quasi-conformally symmetric and $\widetilde{\nabla}$-concircularly symmetric semi-Riemannian manifolds, where $\widetilde{\nabla}$ is metric connection.