Some integral formulae on weighted manifolds

TL;DR

This paper develops new integral formulae for weighted manifolds by introducing a weighted mean sigma-r curvature and employing weighted Newton transformations, generalizing existing flux formulas and applications.

Contribution

The paper introduces a novel notion of weighted mean sigma-r curvature and derives generalized integral formulae on weighted manifolds, extending previous flux formulas.

Findings

Generalized flux formula for weighted manifolds

Introduction of weighted mean sigma-r curvature

Extension of applications of flux formulas

Abstract

Introducing a notion of the weighted mean sigma-r curvature and using the weighted Newton transformations we derive in this paper some integral formulae on weighted manifolds. These formulae generalize the flux formula and some of its examples of applications obtained by Alias, de Lira and Malacarne [3].