Bounds for Eigenvalues of q-Laplacian on Contact Submanifolds of Sasakian Space Forms

Abstract

This study establishes new upper bounds for the mean curvature and constant sectional curvature on Riemannian manifolds for the first positive eigenvalue of the q-Laplacian. In particular, various estimates are provided for the first eigenvalue of the q-Laplace operator on closed orientated (l+1)-dimensional special contact slant submanifolds in a Sasakian space form, M˜2k+1(ϵ), with a constant ψ1-sectional curvature, ϵ. From our main results, we recovered the Reilly-type inequalities, which were proven before this study.

Analyzing Curvature Properties and Geometric Solitons of the Twisted Sasaki Metric on the Tangent Bundle over a Statistical Manifold

“…Gezer, Bilen, and De [25] explored almost Ricci and almost Yamabe soliton structures on the tangent bundle using the ciconia metric. Recently, Li and Khan et al studied solitons, inequalities, and submanifolds using soliton theory, submanifold theory, and other related theories [26][27][28][29][30][31]. They obtained a number of interesting results and inspired the idea of this paper.…”

Chen inequality for general warped product submanifold of Riemannian warped products I×fSm(c)

“…The higher eigenvalues are related to the curvature of the domain and the way it is embedded in Euclidean space. In this sequel, the Dirichlet eigenvalues appear in the solution of the heat equation on a domain and the eigenvalues and the corresponding eigenfunctions determine the rate of decay of the solution [20][21][22][23][24][25][26]. Assume that f is the non-constant warping function on compact warped product submanifold n  .…”

Solitons of η-Ricci–Bourguignon Type on Submanifolds in (LCS)m Manifolds

“…Here, κ signifies a nontrivial smooth function defined on B. This concircular vector field ν earns the title of a concurrent vector field when the specific choice κ = 1 is made within the context of Equation (21). Several mathematicians and researchers have dedicated investigations to exploring manifolds endowed with specific types of vector fields, including [41][42][43].…”

“…The soliton known as η-RB can be simplified to an η-Ricci soliton by setting δ equal to zero in Equation ( 4). Recent works involve soliton types [10][11][12][13], k-almost Yamabe solitons [14], soliton theory [15][16][17][18], singularity theory [19], submanifold theory [20,21], tangent bundle problems [22][23][24][25][26], and classical differential geometry [27,28], all of which have been studied by many mathematicians in recent decades. The main methods, techniques, and results in these papers inspired us to carry out the present research.…”