Stochastic properties of the Laplacian on Riemannian submersions

被引：3

作者：

Cristiane Brandao, M. ^{[1
]}

Oliveira, Jobson Q. ^{[1
]}

机构：

[1] Univ Fed Ceara, Dept Matemat, BR-60455760 Fortaleza, Ceara, Brazil

来源：

GEOMETRIAE DEDICATA | 2013年 / 162卷 / 01期

关键词：

Feller property; Stochastic completeness; Parabolicity; Riemannian immersions and submersions;

D O I：

10.1007/s10711-012-9732-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Based on ideas of Pigolla and Setti (2010), we prove that isometrically immersed submanifolds with bounded mean curvature into Cartan-Hadamard manifolds are Feller. We consider Riemannian submersions pi : M -> N with compact minimal fibers and prove that the total space M is Feller, parabolic or stochastically complete if, and only if, the base manifold N is, respectively, Feller, parabolic or stochastically complete.

引用

页码：363 / 374

页数：12

共 50 条

[1] Stochastic properties of the Laplacian on Riemannian submersions
M. Cristiane Brandão
Jobson Q. Oliveira
Geometriae Dedicata, 2013, 162 : 363 - 374
[2] Eigenforms of the Laplacian for Riemannian V-submersions
Gilkey, P
Kim, HJ
Park, J
TOHOKU MATHEMATICAL JOURNAL, 2005, 57 (04) : 505 - 519
[3] Eigenvalues of the form valued laplacian for Riemannian submersions
Gilkey, PB
Leahy, JV
Park, JH
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1998, 126 (06) : 1845 - 1850
[4] Riemannian submersions which preserve the eigenforms of the Laplacian
Gilkey, PB
Park, JH
ILLINOIS JOURNAL OF MATHEMATICS, 1996, 40 (02) : 194 - 201
[5] On Riemannian submersions
Lempert, L.
ACTA MATHEMATICA HUNGARICA, 2019, 158 (02) : 363 - 372
[6] On Riemannian submersions
L. Lempert
Acta Mathematica Hungarica, 2019, 158 : 363 - 372
[7] The Bochner Laplacian, Riemannian submersions, heat content asymptotics, and heat equation asymptotics
Gilkey, PB
Park, JH
CZECHOSLOVAK MATHEMATICAL JOURNAL, 1999, 49 (02) : 233 - 240
[8] The Bochner Laplacian, Riemannian submersions, heat content asymptotics, and heat equation asymptotics
P. B. Gilkey
J. H. Park
Czechoslovak Mathematical Journal, 1999, 49 : 233 - 240
[9] Biharmonic Riemannian submersions
Mehmet Akif Akyol
Ye-Lin Ou
Annali di Matematica Pura ed Applicata (1923 -), 2019, 198 : 559 - 570
[10] Bounded Riemannian submersions
Tapp, K
INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2000, 49 (02) : 637 - 654

← 1 2 3 4 5 →