Spectral geometry of Riemannian Legendre foliations
We obtain geometric characterizations of isospectral minimal Riemannian Legendre foliations on compact Sasakian manifolds of constant $ϕ$-sectional curvature.
math.DG↗
arXiv subjects
Stere Ianus
Publications and source records attributed to Stere Ianus.
Riemannian submersions from almost contact metric manifolds
In this paper we obtain the structure equation of a contact-complex Riemannian submersion and give some applications of this equation in the study of almost cosymplectic manifolds with Kaehler fibres.
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Submanifolds in manifolds with metric mixed 3-structures
Mixed 3-structures are odd-dimensional analogues of paraquaternionic structures. They appear naturally on lightlike hypersurfaces of almost paraquaternionic hermitian manifolds. We study invariant and anti-invariant submanifolds in a manifold endowed with a mixed 3-structure and a compatible (semi-Riemannian) metric. Particular attention is given to two cases of ambient space: mixed 3-Sasakian and mixed 3-cosymplectic.
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Semi-Riemannian submersions with totally umbilic fibres
We get obstructions to existence of semi-Riemannian submersions with totally umbilic fibres.
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Paraquaternionic CR-submanifolds of paraquaternionic Kahler manifolds and semi-Riemannian submersions
In this paper we introduce paraquaternionic CR-submanifolds of almost paraquaternionic hermitian manifolds and state some basic results on their differential geometry. We also study a class of semi-Riemannian submersions from paraquaternionic CR-submanifolds of paraquaternionic Kaehler manifolds.
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Conformal Killing-Yano Tensors on Manifolds with Mixed 3-Structures
We show the existence of conformal Killing-Yano tensors on a manifold endowed with a mixed 3-Sasakian structure.
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Hidden symmetries and Killing tensors on curved spaces
Higher order symmetries corresponding to Killing tensors are investigated. The intimate relation between Killing-Yano tensors and non-standard supersymmetries is pointed out. In the Dirac theory on curved spaces, Killing-Yano tensors generate Dirac type operators involved in interesting algebraic structures as dynamical algebras or even infinite dimensional algebras or superalgebras. The general results are applied to space-times which appear in modern studies. One presents the infinite dimensional superalgebra of Dirac type operators on the 4-dimensional Euclidean Taub-NUT space that can be seen as a twisted loop algebra. The existence of the conformal Killing-Yano tensors is investigated for some spaces with mixed Sasakian structures.
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Foliations on quaternion CR-submanifolds
The purpose of this paper is to study the canonical foliations of a quaternion CR-submanifold of a quaternion Kähler manifold.
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Some constructions of almost para-hyperhermitian structures on manifolds and tangent bundles
In this paper we give some examples of almost para-hyperhermitian structures on the tangent bundle of an almost product manifold, on the product manifold $M\times\mathbb{R}$, where $M$ is a manifold endowed with a mixed 3-structure and on the circle bundle over a manifold with a mixed 3-structure.
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A Cohomology (p+1) Form Canonically Associated with Certain Codimension-q Foliations on a Riemannian Manifold
Let $(M^{n},g)$ be a closed, connected, oriented, $C^{\infty}$, Riemannian, n-manifold with a transversely oriented foliation $\boldkey F$. We show that if $\lbrace X,Y \rbrace$ are basic vector fields, the leaf component of $[X,Y]$, $\Cal{V}[X,Y]$, has vanishing leaf divergence whenever $κ\wedge χ_{\boldkey F}$ is a closed (possibly zero) de Rham cohomology (p+1)-form. Here $κ$ is the mean curvature one-form of the foliation ${\boldkey F}$ and ${χ_{\boldkey F}}$ is its characteristic form. In the codimension-2 case, $κ\wedge χ_{\boldkey F}$ is closed if and only if $κ$ is horizontally closed. In certain restricted cases, we give necessary and sufficient conditions for $κ\wedge{χ_{\boldkey F}}$ to be harmonic. As an application, we give a characterization of when certain closed 3-manifolds are locally Riemannian products. We show that bundle-like foliations with totally umbilical leaves with leaf dimension greater than or equal to two on a constant curvature manifold, with non-integrable transversal distribution, and with Einstein-like transversal geometry are totally geodesic.
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Semi-Riemannian submersions with totally umbilic fibres
We get obstructions to existence of semi-Riemannian submersions with totally umbilic fibres.
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Semi-Riemannian submersions from real and complex pseudo-hyperbolic spaces
We classify the semi-Riemannian submersions from a pseudo-hyperbolic space onto a Riemannian manifold under the assumption that the fibres are connected and totally geodesic. Also we obtain the classification of the semi-Riemannian submersions from a complex pseudo-hyperbolic space onto a Riemannian manifold under the assumption that the fibres are complex, connected and totally geodesic submanifolds.
math.DG↗