Communications of the
Korean Mathematical Society

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024



Commun. Korean Math. Soc. 2010; 25(2): 235-243

Printed June 1, 2010

Copyright © The Korean Mathematical Society.

On almost $r$-paracontact Riemannian manifold with a certain connection

Mobin Ahmad, Abdul Haseeb, Jae-Bok Jun, and Shamsur Rahman

Integral University, Integral University, Kook-Min University, and Integral University


In a Riemannian manifold, the existence of a new connection is proved. In particular cases, this connection reduces to several symmetric, semi-symmetric and quarter symmetric connections, even some of them are not introduced so far. So, in this paper, we define a quarter symmetric semi-metric connection in an almost $r$-paracontact Riemannian manifold and consider invariant, non-invariant and anti-invariant hypersurfaces of an almost $r$-paracontact Riemannian manifold with that connection.

Keywords: almost $r$-paracontact Riemannian manifold, quarter-symmetric semi-metric connection

MSC numbers: 53C05, 53D12

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