arXiv subjects

Miroslava Petrović-Torgašev

Publications and source records attributed to Miroslava Petrović-Torgašev.

5 recordsLinked to original sources

arXiv2025

Curvature properties of pseudosymmetry type of some 2-quasi-Einstein manifolds

Let (M,g) be a 2-quasi-Einstein non-conformally flat semi-Riemannian manifold of dimension > 3. We prove that if its Riemann-Christoffel curvature tensor R is a linear combination of some Kulkarni-Nomizu tensors formed by the metric tensor g, the Ricci tensor S and its square S^2, then some pseudosymmetry type curvature conditions are satisfied. Certain non-conformally flat warped product manifolds with 2-dimensional base, and in particular some spacetimes, are such 2-quasi Einstein manifolds.

math.DG↗

arXiv2023

On Thurston's geometrical space form problem: on quasi space forms

A proposal is made for what may well be the most elementary Riemannian spaces which are homogeneous but not isotropic. In other words: a proposal is made for what may well be the nicest symmetric spaces beyond the real space forms, that is, beyond the Riemannian spaces which are homogeneous and isotropic. The above qualification of `'nicest symmetric spaces'' finds a justification in that, together with the real space forms, these spaces are most natural with respect to the importance in human vision of our ability to readily recognise conformal things and in that these spaces are most natural with respect to what in Weyl's view is symmetry in Riemannian geometry. Following his suggestion to remove the real space forms' isotropy condition, the quasi space forms thus introduced do offer a metrical, local geometrical solution to the geometrical space form problem as posed by Thurston in his 1979 Princeton Lecture Notes on `'The Geometry and Topology of 3-manifolds''. Roughly speaking, quasi space forms are the Riemannian manifolds of dimension greater than or equal to 3, which are not real space forms but which admit two orthogonally complementary distributions such that at all points all the 2-planes that in the tangent spaces there are situated in a same position relative to these distributions do have the same sectional curvatures.

math.DG↗

arXiv2023

On Wintgen ideal submanifolds satisfying some pseudo-symmetry type curvature conditions

Let M be a Wintgen ideal submanifold of dimension n in a real space form R^{n+m}(k) of dimension (n+m) and of constant curvature k, n > 3, m = 1 or m > 1. Let g, R, Ricc, g /\ Ricc and C be the metric tensor, the Riemann-Christoffel curvature tensor, the Ricci tensor, the Kulkarni-Nomizu product of g and Ricc, and the Weyl conformal curvature tensor of M, respectively. In this paper we study Wintgen ideal submanifolds M in real space forms R^{n+m}(k), n > 3, m = 1 or m > 3, satisfying the following pseudo-symmetry type curvature conditions: (i) R.C and Q(g,R) (resp., Q(g,C), Q(g,g/\Ricc), Q(Ricc,R) or Q(Ricc,g/\Ricc)) are linearly dependent; (ii) C.R and Q(g,R) (resp., Q(g,C), Q(g,g/\Ricc), Q(Ricc,R) or Q(Ricc,g/\Ricc)) are linearly dependent; (iii) R.C - C.R and Q(g,R) (resp., Q(g,C), Q(g,g/\Ricc), Q(Ricc,R) or Q(Ricc,g/\Ricc)) are linearly dependent.

math.DG↗

arXiv2023

On semi-Riemannian manifolds satisfying some generalized Einstein metric conditions

The difference tensor R.C-C.R of a semi-Riemannian manifold (M,g), dim M > 3, formed by its Riemannian-Christoffel curvature tensor R and the Weyl conformal curvature tensor C, under some assumptions, can be expressed as a linear combination of (0,6)-Tachibana tensors Q(A,T), where A is a symmetric (0,2)-tensor and T a generalized curvature tensor. These conditions form a family of generalized Einstein metric conditions. In this survey paper we present recent results on manifolds and submanifolds, and in particular hypersurfaces, satisfying such conditions.

math.DG↗

arXiv2023

A note on some generalized curvature tensor

For any semi-Riemannian manifold (M,g) we define some generalized curvature tensor as a linear combination of Kulkarni-Nomizu products formed by the metric tensor, the Ricci tensor and its square of given manifold. That tensor is closely related to quasi-Einstein spaces, Roter spaces and some Roter type spaces.

math.DG↗