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• ANTI-INVARIANT SUBMANIFOLDS OF (є) –SASAKIAN MANIFOLD

Channabasappa Shanthappa Bagewadi, S. Shashikala Venkatesha

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Abstract

T he object of the present paper is to study anti-invariant submanifolds M of (є) - Sasakian manifold . It is shown that if M is totally umbilical then M is totally geodesic. Also results have been obtained connecting   totally geodesicty and   anti-invariance of M. Also  we  find  the necessary  and  sufficient condition for  anti-invariant  submanifolds of (є)-Sasakian  manifold  to be T -invariant and anti-invariant and condition  for  integrability of the  distribution D .

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What this paper is about

T he object of the present paper is to study anti-invariant submanifolds M of (є) - Sasakian manifold . It is shown that if M is totally umbilical then M is totally geodesic. Also results have been obtained connecting   totally geodesicty and   anti-invariance of M. Also  we  find  the necessary  and  sufficient condition for  anti-invariant  submanifolds of (є)-Sasakian  manifold  to be T -invariant and anti-invariant and condition  for  integrability of the  distribution D .

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Available abstract

T he object of the present paper is to study anti-invariant submanifolds M of (є) - Sasakian manifold . It is shown that if M is totally umbilical then M is totally geodesic. Also results have been obtained connecting   totally geodesicty and   anti-invariance of M. Also  we  find  the necessary  and  sufficient condition for  anti-invariant  submanifolds of (є)-Sasakian  manifold  to be T -invariant and anti-invariant and condition  for  integrability of the  distribution D .

Key concepts: Invariant (physics), Totally geodesic, Invariant manifold, Mathematics, Pure mathematics, Manifold (fluid mechanics), Geodesic, Mathematical analysis

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