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Clairaut Generic Riemannian Maps from Nearly Kahler Manifolds

Nidhi Yadav, Kirti Gupta, Punam Gupta

Abstract

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.

Clairaut Generic Riemannian Maps from Nearly Kahler Manifolds

Abstract

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.

Paper Structure

This paper contains 4 sections, 8 theorems, 89 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Riemannian Maps
  4. Clairaut Generic Riemannian Map

Key Result

Theorem 3.2

Bishop Let $F :(M,g_{1})\rightarrow (N,g_{2})$ be a Riemannian map with connected fibers. Then, $F$ is a Clairaut Riemannian map with $\tilde{r}=e^{f}$ if and only if each fiber is totally umbilical and has the mean curvature vector field $H=-{\operatorname{grad}}f$, where ${\operatorname{grad}}f$ i

Theorems & Definitions (13)

  • Definition 2.1
  • Definition 3.1
  • Theorem 3.2
  • Definition 3.3
  • Lemma 3.4
  • Theorem 3.5
  • Theorem 3.6
  • Corollary 3.7
  • Lemma 3.8
  • Proposition 3.9
  • ...and 3 more