Curvature Identities for Generalized Kenmotsu Manifolds

S Uvarova,Ivan Kochetkov,Aligadzhi Rustanov,Abu-Saleem Ahmad,V Breskich

doi:10.1051/e3sconf/202124409005

Abstract

In the present paper we obtained 2 identities, which are satisfied by Riemann curvature tensor of generalized Kenmotsu manifolds. There was obtained an analytic expression for third structure tensor or tensor of f-holomorphic sectional curvature of GK-manifold. We separated 2 classes of generalized Kenmotsu manifolds and collected their local characterization.

Highlights

Let M be a connected smooth manifold of (2n+1) dimension, CC∞(MM) is the algebra of smooth functions on M, XX(MM) - CC∞ - module of smooth vector fields on M, d is the operator of exterior differentiation
We recall [1] that a contact form or contact structure on an odd-dimensional manifold M, dim MM = 2nn + 1, is called 1-form on M, which in each point of the manifold is ηη ∧ (⏟dddd) ∧ ... ∧ ≠ 0, i.e. rrrrrr = dim MM is in each point of M
It is easy to derive from Darboux theorem [1] that L ∩ M = {0}, XX(MM) = L⨁M

Summary

Introduction

Let M be a connected smooth manifold of (2n+1) dimension, CC∞(MM) is the algebra of smooth functions on M, XX(MM) - CC∞ - module of smooth vector fields on M, d is the operator of exterior differentiation. The most important example of almost contact metric structures, which largely determines their role in differential geometry, is the structure induced on the hypersurface N of the manifold M equipped with an almost Hermitian structure {JJ, 〈∙,∙〉} For example, naturally arise in the Tanno classification of connected almost contact metric manifolds such that automorphism group has maximum dimension [8]. They have a number of remarkable properties. We continue the study of generalized Kenmotsu manifolds and investigate the geometry of the Riemannian curvature tensor for this class of manifolds. We get a local characterization of these classes

Preliminaries

Generalized Kenmotsu manifolds

Curvature identities for GK-manifolds