# Yamabe flow on modified Riemann extension

## TL;DR

This paper investigates how various curvature tensors evolve under Yamabe flow, focusing on modified Riemann extensions and their behavior, with implications for standard metrics in differential geometry.

## Contribution

It introduces the study of modified Riemann extensions under Yamabe flow and analyzes the evolution of curvature tensors, providing new insights into geometric flows on extended manifolds.

## Key findings

- Rate relations of curvature tensors under Yamabe flow are established.
- Modified Riemann extensions exhibit specific behaviors under Yamabe flow.
- Remarks on standard metrics highlight special cases and applications.

## Abstract

In this paper the rate relations of Riemann, conformal, conharmonic and Weyl curvature tensors under Yamabe flow are studied. Modified Riemann extensions under Yamabe flow is discussed. The paper ends with remarks on some standard metrics.