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Universal Bundles of Metrics and Polymetrics: A Generalization
Shouvik Datta Choudhury
We formalize the ``metric bundle'' viewpoint by defining, for any smooth --manifold , the open fiberwise cones $\mathcal{G}^{p,q}\subset S^2\Tstar M$ of nondegenerate symmetr…
Some generalized inequalities in Riemannian Geometry
Shouvik Datta Choudhury
[1] investigates advanced connotations of Hardy and Rellich-type inequalities on complete noncompact Riemannian manifolds, delving on deriving inequalities that incorporate poignan…
Evolution and Monotonicity of Geometric Constants under Extended Ricci Flows with Variable Coupling Parameters
Shouvik Datta Choudhury
This paper explores the evolution and monotonicity of geometric constants within the framework of extended Ricci flows, incorporating variable coupling parameters. Building on Hami…
Evolution of Functionals Under Extended Ricci Flow
Shouvik Datta Choudhury
In this paper, we investigate the evolution of certain functionals involving higher powers of a scalar quantity under Bernard List's extended Ricci flow on a compact Riemannian…
Riemannian Metric Bundle
Shouvik Datta Choudhury
A Riemannian metric bundle G(M) is a fiber bundle over a smooth manifold M, whose fibers are the spaces of symmetric, positive-definite bilinear forms on the tangent spaces of M, w…
2-Radical Laplace Operators
Shouvik Datta Choudhury
The paper introduces a new elliptic operator called the two-radical Laplace operator, which has a positive eigenvalue equal to the positive square root of the eigenvalue of the Lap…
Root Laplacian Eigenmaps with their application in spectral embedding
Shouvik Datta Choudhury
The root laplacian operator or the square root of Laplacian which can be obtained in complete Riemannian manifolds in the Gromov sense has an analog in graph theory as a square roo…