In this paper, we study $(k,\mu)$-contact metric manifold under $D_a$-homothetic deformation. It is proved that a $D_3$-homothetic deformed locally symmetric $(1, -4)$-contact metric manifold is a Sasakian manifold and the Ricci soliton is shrinking. Further, $\xi^*$-projectively flat and $h$-projectively semisymmetric $(k, \mu)$-contact metric manifolds under $D_a$-homothetic deformation are studied and obtained interesting results.
$D_{a}$-homothetic deformation Ricci solitons projective curvature tensor $D_{a}$-homothetic deformation Ricci solitons projective curvature tensor
Primary Language | English |
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Subjects | Engineering |
Journal Section | Articles |
Authors | |
Publication Date | April 15, 2019 |
Submission Date | August 7, 2018 |
Acceptance Date | December 6, 2018 |
Published in Issue | Year 2019 Volume: 7 Issue: 1 |