Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
|
   
Available in electronic format
Available in print format 		Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(e) ISSN 0002-9939(p)

     

Topological entropy for geodesic flows under a Ricci curvature condition

Author(s): Seong-Hun Paeng
Journal: Proc. Amer. Math. Soc. 125 (1997), 1873-1879.
MSC (1991): Primary 58F17; Secondary 53C20, 53C21, 53C22
MathSciNet review: 1372043
Retrieve article in: PDF
This article is available free of charge

Abstract | References | Similar articles | Additional information

Abstract: It is known that the topological entropy for the geodesic flow on a Riemannian manifold $M$ is bounded if the absolute value of sectional curvature $|K_{M}|$ is bounded. We replace this condition by the condition of Ricci curvature and injectivity radius.

References:

[AC]
M. Anderson, J. Cheeger, $C^{\alpha }$-compactness for manifolds with Ricci curvature and injectivity radius bounded below, J. Differential Geometry 35 (1992), 265-281. MR 93c:53028

[B]
R. Brocks, Abstandsfunktion, Riccikrümmung und Injektivitätsradius, Diplomarbeit, University of Münster (1993).

[CE]
J. Cheeger, D. G. Ebin, Comparison theorems in Riemannian geometry, Amsterdam, 1975. MR 56:16538

[DSW]
X. Dai, Z. Shen, G. Wei, Negative Ricci curvature and isometry group, Duke Math. J. 76 (1994), 59-73. MR 96e:53051

[FM]
A. Freire, R. Mañé, On the entropy of geodesic flow in manifolds without conjugate points, Invent. Math. 69 (1982), 375-392. MR 84d:58063

[GHL]
S. Gallot, D. Hulin, J. Lafontaine, Riemannian geometry, Springer-Verlag, 1987. MR 88k:53001

[H]
J. Heo, Completely multi-positive linear maps and representations of Hilbert $C^{*}$-modules, preprint.

[KH]
A. B. Katok, B. Hasselblatt, Introduction to the modern theory of dynamical systems, Cambridge University Press, 1995. MR 96c:58055

[Ma1]
A. Manning, Topological entropy for geodesic flows, Ann. Math. 110 (1979), 567-573. MR 81e:58044

[Ma2]
-, More topological entropy for geodesic flows, Dynamical systems and turbulence, Warwick (1980), 243-250. MR 84j:58096

[P]
S.-H. Paeng, A sphere theorem under a curvature perturbation, Kyushu J. Math. 50 (1996), 459-470.

Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 58F17, 53C20, 53C21, 53C22

Retrieve articles in all Journals with MSC (1991): 58F17, 53C20, 53C21, 53C22

Additional Information:

Seong-Hun Paeng
Affiliation: Department of Mathematics, Seoul National University, Seoul 151-742, Korea
Email: shpaeng@math.snu.ac.kr

DOI: 10.1090/S0002-9939-97-03780-5
PII: S 0002-9939(97)03780-5
Received by editor(s): August 23, 1995
Received by editor(s) in revised form: October 17, 1995 and December 21, 1995
Additional Notes: Partially supported by the Basic Science Research Institute Program and in part supported by GARC-KOSEF
Communicated by: Mary Rees
Copyright of article: Copyright 1997, American Mathematical Society




AMS and Social Media LinkedIn Facebook Podcasts Twitter YouTube RSS Feeds Blogs Wikipedia