Résultats de recherche pour « Pseudo-Riemannian Manifolds »
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A submanifold of a Riemannian manifold is called a parallel submanifold if its second fundamental form is parallel with respect to the van der Waerden–Bortolotti connection. From submanifold point of view, parallel submanifolds are the simplest Riemannian submanifolds next to …
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A submanifold of a Riemannian manifold is called a parallel submanifold if its second fundamental form is parallel with respect to the van der Waerden–Bortolotti connection. From submanifold point of view, parallel submanifolds are the simplest Riemannian submanifolds next to totally geodesic ones. Parallel submanifolds form an important class of Riemannian submanifolds since extrinsic invariants of a parallel submanifold do not vary from point to point. In this paper, we provide a comprehensive survey on this important class of submanifolds.
Abstract We study some properties of curvature tensors of Norden and, more generally, metallic pseudo-Riemannian manifolds. We introduce the notion of J -sectional and J -bisectional curvature of a metallic pseudo-Riemannian manifold ( M , J , g ) and …
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Abstract We study some properties of curvature tensors of Norden and, more generally, metallic pseudo-Riemannian manifolds. We introduce the notion of J -sectional and J -bisectional curvature of a metallic pseudo-Riemannian manifold ( M , J , g ) and study their properties.We prove that under certain assumptions, if the manifold is locally metallic, then the Riemann curvature tensor vanishes. Using a Norden structure ( J , g ) on M , we consider a family of metallic pseudo-Riemannian structures { J a,b } a , b ∈ℝ and show that for a ≠ 0, the J -sectional and J -bisectional curvatures of M coincide with the J a , b -sectional and J a , b -bisectional curvatures, respectively. We also give examples of Norden and metallic structures on ℝ 2 n .
We construct a local framework for maps between pseudo-Riemannian manifolds of different dimensions that preserve null directions. Let \( F: M_i \to M_{i+1} \); F is null-preserving if \( F_* v \) is null for every null \( v \in …
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We construct a local framework for maps between pseudo-Riemannian manifolds of different dimensions that preserve null directions. Let \( F: M_i \to M_{i+1} \); F is null-preserving if \( F_* v \) is null for every null \( v \in T_p M_i \). Deviations from an exact metric pullback are measured via a correction tensor T. This setup extends Liouville-type uniqueness results to the interdimensional case, providing a precise tool for local analysis of geometric embeddings.
We study the characteristics of affine vector fields on pseudo-Riemannian manifolds and provide tensorial formulas that characterize these vector fields. Using our approach, we present a straightforward proof that any affine vector field on a compact Riemannian manifold is a …
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We study the characteristics of affine vector fields on pseudo-Riemannian manifolds and provide tensorial formulas that characterize these vector fields. Using our approach, we present a straightforward proof that any affine vector field on a compact Riemannian manifold is a Killing vector field. Moreover, we establish several necessary and sufficient conditions for an affine vector field on a Riemannian manifold to be classified as a Killing or parallel vector field.