The weighted Laplacians on real and complex metric measure spaces
Differential Geometry
2014-04-10 v2
Abstract
In this short note we compare the weighted Laplacians on real and complex (K\"ahler) metric measure spaces. In the compact case K\"ahler metric measure spaces are considered on Fano manifolds for the study of K\"ahler-Einstein metrics while real metric measure spaces are considered with Bakry-\'Emery Ricci tensor. There are twisted Laplacians which are useful in both cases but look alike each other. We see that if we consider noncompact complete manifolds significant differences appear.
Keywords
Cite
@article{arxiv.1312.7607,
title = {The weighted Laplacians on real and complex metric measure spaces},
author = {Akito Futaki},
journal= {arXiv preprint arXiv:1312.7607},
year = {2014}
}
Comments
Minor modifications. Submitted to Shoshichi Kobayashi memorial volume