• A New Proof of the Theorem: Harmonic Manifolds with Minimal Horospheres are Flat

• # Fulltext

https://www.ias.ac.in/article/fulltext/pmsc/124/03/0419-0425

• # Keywords

Harmonic manifold; Busemann function; minimal horospheres.

• # Abstract

In this note we reprove the known theorem: Harmonic manifolds with minimal horospheres are flat. It turns out that our proof is simpler and more direct than the original one. We also reprove the theorem: Ricci flat harmonic manifolds are flat, which is generally affirmed by appealing to Cheeger–Gromov splitting theorem. We also confirm that if a harmonic manifold 𝑀 has same volume density function as $\mathbb{R}^n$, then 𝑀 is flat.

• # Author Affiliations

1. Harish Chandra Research Institute, Chhatnag Road, Jhusi 211 019, India

• # Proceedings – Mathematical Sciences

Volume 132, 2022
All articles
Continuous Article Publishing mode

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019