Uday Chand De

Characterizations of twisted spacetimes

Twisted spacetimes generalize Robertson-Walker cosmological models by allowing the scale factor to depend on both spatial position and time, thereby modeling inhomogeneous cosmic expansion. This article establishes geometric conditions under which a Lorentzian manifold becomes a...

The Sobolev inequalities along the Ricci-Bourguignon flow and applications

‎Consider a closed Riemannian manifold $M$ where the metrics $g(t)$ evolve by the Ricci-Bourguignon flow (RBF)‎.‎The paper first derives a Sobolev inequality along the RBF‎. ‎Then‎, ‎by applying this‎ ‎Sobolev inequality we obtain a linear parabolic estimate and an upper bound es...