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Advances in Pure and Applied Mathematics

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Some curvature properties of paracontact metric manifolds

Krishanu Mandal
  • Corresponding author
  • Department of Pure Mathematics, University of Calcutta, 35, Ballygunge Circular Road, Kolkata 700019, West Bengal, India
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/ Uday Chand De
  • Department of Pure Mathematics, University of Calcutta, 35, Ballygunge Circular Road, Kolkata 700019, West Bengal, India
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Published Online: 2017-10-24 | DOI: https://doi.org/10.1515/apam-2017-0064

Abstract

The purpose of this paper is to study Ricci semisymmetric paracontact metric manifolds satisfying ξh=0 and such that the sectional curvature of the plane section containing ξ equals a non-zero constant c. Also, we study paracontact metric manifolds satisfying the curvature condition QR=0, where Q and R are the Ricci operator and the Riemannian curvature tensor, respectively, and second order symmetric parallel tensors in paracontact metric manifolds under the same conditions. Several consequences of these results are discussed.

Keywords: Paracontact metric manifolds; Ricci semisymmetric; second order parallel tensor,Einstein manifold

MSC 2010: 53B30; 53C15; 53C25; 53D10; 53D15

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About the article

Received: 2017-05-31

Revised: 2017-09-16

Accepted: 2017-10-02

Published Online: 2017-10-24

Published in Print: 2018-07-01


Citation Information: Advances in Pure and Applied Mathematics, Volume 9, Issue 3, Pages 159–165, ISSN (Online) 1869-6090, ISSN (Print) 1867-1152, DOI: https://doi.org/10.1515/apam-2017-0064.

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