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Dualistic Structures on Twisted Product Manifolds

Abdoul Salam Diallo, Leonard Todjihounde

Abstract

In this paper, we show that the projection of a dualistic structure defined on a twisted product manifold induces dualistic structures on the base and the fiber manifolds, and conversely. Then under some conditions on the Ricci curvature and the Weyl conformal tensor we characterize dually flat structures on twisted product manifolds.

Dualistic Structures on Twisted Product Manifolds

Abstract

In this paper, we show that the projection of a dualistic structure defined on a twisted product manifold induces dualistic structures on the base and the fiber manifolds, and conversely. Then under some conditions on the Ricci curvature and the Weyl conformal tensor we characterize dually flat structures on twisted product manifolds.

Paper Structure

This paper contains 6 sections, 18 theorems, 28 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Dualistic structures
  4. Twisted product manifolds
  5. Dualistic structures on twisted product manifolds
  6. Dually flat twisted product manifolds

Key Result

Proposition 2.1

The torsion tensors $T^{\nabla}$ and $T^{\nabla^*}$ of $\nabla$ and $\nabla^*$, respectively, satisfy: for any $X,Y, Z \in \Gamma(TM)$.

Theorems & Definitions (26)

  • Proposition 2.1
  • proof
  • Corollary 2.1
  • Proposition 2.2
  • proof
  • Corollary 2.2
  • Proposition 2.3
  • Corollary 2.3
  • Lemma 2.1
  • Proposition 2.4: FGKU
  • ...and 16 more