This paper studies the contact CR-warped product submanifolds of a generalized Sasakian space form admitting a nearly cosymplectic structure. Some inequalities for the existence of these types of warped product submanifolds are established, the obtained inequalities generalize the results that have acquired in \cite{atceken14}. Moreover, we also estimate another inequality for the second fundamental form in the expressions of the warping function, this inequality also generalizes the inequalities that have obtained in \cite{ghefari19}. In addition, we also explore the equality cases.
In this article, we obtain improved Chen-Ricci inequalities for submanifolds of generalized space forms with quarter-symmetric metric connection, with the help of which we completely characterized the Lagrangian submanifold in generalized complex space form and a Legendrian submanifold in a generalized Sasakian space form. We also discuss some geometric applications of the obtained results.
In this paper, we find the second variational formula for a generalized Sasakian space form admitting a semisymmetric metric connection. Inequalities regarding the stability criteria of a compact generalized Sasakian space form admitting a semisymmetric metric connection are established.
In the present paper, by considering the Gauss equation in place of the Codazzi equation, we derive new optimal inequality for the second fundamental form of CR-warped product submanifolds into a generalized Sasakian space form. Moreover, the inequality generalizes some inequalities for various ambient space forms.
The object of this paper is to study symmetric properties of Sasakian generalized Sasakian-space-form with respect to generalized Tanaka–Webster connection. We studied semisymmetry and Ricci semisymmetry of Sasakian generalized Sasakian-space-form with respect to generalized Tanaka–Webster connection. Further we obtain results for Ricci pseudosymmetric and Ricci-generalized pseudosymmetric Sasakian generalized Sasakian-space-form.
The objective of this paper is to achieve the inequality for Ricci curvature
of a contact CR-warped product submanifold isometrically immersed in a
generalized Sasakian space form admitting a trans-Sasakian structure in the
expressions of the squared norm of mean curvature vector and warping
function. We provide numerous physical applications of the derived
inequalities. Finally, we prove that under a certain condition the base
manifold is isometric to a sphere with a constant sectional curvature.
In this paper, we characterize N(k)-contact metric manifolds with generalized
Tanaka-Webster connection. We obtain some curvature properties. It is proven
that if an N(k)-contact metric manifold with generalized Tanaka-Webster
connection is K-contact then it is an example of generalized Sasakian space
form. Also, we examine some flatness and symmetric conditions of concircular
curvature tensor on an N(k)-contact metric manifolds with generalized
Tanaka-Webster connection.
In this paper we study τ-curvature tensor in generalized Sasakian-space-form. We study semisymmetric generalized Sasakian-space-form and obtain results for particular cases. We also study generalized Sasakian-space-form satisfying . We also obtain some results for all particular cases of τ -Curvature tensor.
Characterizing inequalities for existence of contact CR-warped product submanifolds of generalized Sasakian space forms admitting a nearly cosymplectic structure
