Invariant Submanifolds of A (k,mu)-Paracontact Metric Manifold

Abstract

In this paper, we research some geometric conditions for an
invariant submanifold of a (·; ¹)-paracontact metric manifold to be to-
tally geodesic. Besides this, we characterize an invariant submanifold of a
(·; ¹)-paracontact metric manifold satisfying the conditions Q(S; ¾) = 0,
Q(S;r¾) = 0, Q(S;R ¢ ¾) = 0, Q(g;C ¢ ¾) = 0 and Q(S;C ¢ ¾) = 0 under
the some conditions.