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Certain results on a type of contact metric manifold
U C DE, A Ã‡ETINKAYA
Published in Springer Verlag
2015
Volume: 26

Issue: 43654
Pages: 1229 - 1236
Abstract
Let $$M$$M be a $$3$$3-dimensional almost contact metric manifold satisfying $$(*)$$(∗) condition. We denote such a manifold by $$M^{*}$$M∗. At first we study symmetric and skew-symmetric parallel tensor of type $$(0,2)$$(0,2) in $$M^{*}$$M∗. Next we prove that a non-cosymplectic manifold $$M^{*}$$M∗ is Ricci semisymmetric if and only if it is Einstein. Also we study locally $$\phi$$ϕ-symmetry and $$\eta$$η-parallel Ricci tensor of $$M^{*}$$M∗. Finally, we prove that if a non-cosymplectic $$M^{*}$$M∗ is Einstein, then the manifold is Sasakian. © 2014, African Mathematical Union and Springer-Verlag Berlin Heidelberg.