On the Curvature and Heat Flow on Hamiltonian Systems

Shin-ichi Ohta

Analysis and Geometry in Metric Spaces (2014)

  • Volume: 2, Issue: 1, page 81-114, electronic only
  • ISSN: 2299-3274

Abstract

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We develop the differential geometric and geometric analytic studies of Hamiltonian systems. Key ingredients are the curvature operator, the weighted Laplacian, and the associated Riccati equation.We prove appropriate generalizations of the Bochner-Weitzenböck formula and Laplacian comparison theorem, and study the heat flow.

How to cite

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Shin-ichi Ohta. "On the Curvature and Heat Flow on Hamiltonian Systems." Analysis and Geometry in Metric Spaces 2.1 (2014): 81-114, electronic only. <http://eudml.org/doc/267463>.

@article{Shin2014,
abstract = {We develop the differential geometric and geometric analytic studies of Hamiltonian systems. Key ingredients are the curvature operator, the weighted Laplacian, and the associated Riccati equation.We prove appropriate generalizations of the Bochner-Weitzenböck formula and Laplacian comparison theorem, and study the heat flow.},
author = {Shin-ichi Ohta},
journal = {Analysis and Geometry in Metric Spaces},
keywords = {Hamiltonian; curvature; comparison theorem; heat flow},
language = {eng},
number = {1},
pages = {81-114, electronic only},
title = {On the Curvature and Heat Flow on Hamiltonian Systems},
url = {http://eudml.org/doc/267463},
volume = {2},
year = {2014},
}

TY - JOUR
AU - Shin-ichi Ohta
TI - On the Curvature and Heat Flow on Hamiltonian Systems
JO - Analysis and Geometry in Metric Spaces
PY - 2014
VL - 2
IS - 1
SP - 81
EP - 114, electronic only
AB - We develop the differential geometric and geometric analytic studies of Hamiltonian systems. Key ingredients are the curvature operator, the weighted Laplacian, and the associated Riccati equation.We prove appropriate generalizations of the Bochner-Weitzenböck formula and Laplacian comparison theorem, and study the heat flow.
LA - eng
KW - Hamiltonian; curvature; comparison theorem; heat flow
UR - http://eudml.org/doc/267463
ER -

References

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