Summary
We prove a theorem about an extremal property of Lobachevsky space among simply connected Riemannian manifolds of nonpositive curvature.
I thank the referee for some helpful comments and for correcting my English style.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
J. Hadamard, Sur certaines propriétes des trajectories en dynamique, S. Muth. Pures. Apple, 3 (1897), 331–387.
S. S. Chern, R. K. Lashof, The total curvature of immersed manifolds, Amer. S. Math., (1957), 79, 308–318.
S. Alexander, Locally convex hypersurfaces of negatively curved spaces, Proc. Amer. Math. Soc., (1977), 64,(2), 321–325.
S. Heijenort, On locally convex manofolds, Comm. Pure Appl. Maths, (1952), 5, 223–242.
R. Currier, On hypersurfaces of hyperbolic space infinitesimally supported by horospheres, Trans. Amer. Math. Soc., (1989), 313,(1), 412–431.
A. A. Borisenko, D. I. Vlasenko, Convex surfaces in Lobachevsky space, Math. Physics, Analysis, Geometry, (1997), 4,(3), 278–285.
S. A. Scherbakov, Regularity of radial field on Hadamard manifold which clamped sectional curvature and bounded geometry, VINITI, dep. (3815-81), (1981), 30.
A. A. Borisenko, Convex sets in Hadamard manifolds, Differential Geometry and its Applications, (2002), 17, 111–121.
A. A. Borisenko, V. Miquel, Comparison theorems on convex hypersurfaces in Hadamard manifolds, Ann. Global Anal. Geom., (2002), 21, 191–202.
L. P. Eisenhart, Riemannian geometry, Princeton University Press. Princeton, (1949).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Additional information
Dedicated to Professor Lieven Vanhecke
Rights and permissions
Copyright information
© 2005 Birkhäuser Boston
About this chapter
Cite this chapter
Borisenko, A.A. (2005). Convex Hypersurfaces in Hadamard Manifolds. In: Kowalski, O., Musso, E., Perrone, D. (eds) Complex, Contact and Symmetric Manifolds. Progress in Mathematics, vol 234. Birkhäuser Boston. https://doi.org/10.1007/0-8176-4424-5_3
Download citation
DOI: https://doi.org/10.1007/0-8176-4424-5_3
Publisher Name: Birkhäuser Boston
Print ISBN: 978-0-8176-3850-4
Online ISBN: 978-0-8176-4424-6
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)