Ricci solitons (RS) have an extensive background in modern physics and are extensively used in cosmology and general relativity. The focus of this work is to investigate Ricci almost solitons (RAS) on Lorentzian manifolds with a special metric connection called a semi-symmetric metric u-connection (SSM-connection). First, we show that any quasi-Einstein Lorentzian manifold having a SSM-connection, whose metric is RS, is Einstein manifold. A similar conclusion also holds for a Lorentzian manifold with SSM-connection admitting RS whose soliton vector Z is parallel to the vector u. Finally, we examine the gradient Ricci almost soliton (GRAS) on Lorentzian manifold admitting SSM-connection.

The object of the present paper is to study submanifolds of (k, µ)-contact manifolds. We find the necessary and sufficient conditions for a submanifolds of (k, µ)-contact manifolds to be invariant and anti-invariant. Also, we examine the integrability of the distributions involved in the definition of CR-submanifolds of (k, µ)-contact manifolds. RESUMEN El objeto del presente artículo es estudiar subvariedades de variedades (k, µ)-contacto. Encontramos las condiciones necesarias y suficientes para que subvariedades de variedades (k, µ)-contacto sean invariantes y anti-invariantes. También examinamos la integrabilidad de las distribuciones involucradas en la definición de subvariedades CR de variedades (k, µ)-contacto.

In the present paper we have studied invariant submanifolds of a-contact manifold admitting quarter symmetric metric connection and obtained some interesting results.