Almost Hermitian Manifold with Quarter Symmetric Non-Metric Connection

Abstract

In this research, certain results for an almost Hermite manifold
equipped with a quarter symmetric non-metric connection has been
mentioned. A part from finding the necessary and sufficient condition for
a covariant almost analytic vector field with respect to Riemannian
connection D to be covariant almost analytic with respect to quarter
symmetric non-metric connection  , it has also been shown that Nijenhuis
tensor with respect to the connection  on an almost Hermite manifold
equipped with a quarter symmetric non-metric connection is equal to the
Nijenhuis tensor with respect to the Riemannian connection. The geodesics
on an almost Hermite manifold equipped with quarter symmetric nonmetric
connection has also been discussed.