Chen Inequalities for Warped Product Pointwise Bi-Slant Submanifolds of Complex Space Forms and Its Applications

Abstract

In this paper, by using new-concept pointwise bi-slant immersions, we derive a fundamental inequality theorem for the squared norm of the mean curvature via isometric warped-product pointwise bi-slant immersions into complex space forms, involving the constant holomorphic sectional curvature c, the Laplacian of the well-defined warping function, the squared norm of the warping function, and pointwise slant functions. Some applications are also given.

Geometrical Structure in a Perfect Fluid Spacetime with Conformal Ricci–Yamabe Soliton

“…Many authors ( [8][9][10][11][12][13]) have studied Ricci soliton and Yamabe soliton on contact manifolds. Furthermore, some researchers have also studied conformal η-Ricci solitons, singular submanifolds, biharmonic submanifolds, warped product pointwise semislant submanifolds and so on [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33]. In recent years, Kumara, H. A. studied and determined geometrical aspects of perfect fluid spacetime with torse-forming vector field and Ricci soliton in perfect fluid spacetime with torse-forming vector field ξ.…”