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Total absolute horospherical curvature of submanifolds in hyperbolic space
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Marcelo Buosi
Veröffentlicht/Copyright:
10. August 2010
Abstract
We study the horospherical geometry of submanifolds in hyperbolic space. The main result is a formula for the total absolute horospherical curvature of M, which implies, for the horospherical geometry, the analogues of classical inequalities of the Euclidean Geometry. We prove the horospherical Chern–Lashof inequality for surfaces in 3-space and the horospherical Fenchel and Fary–Milnor's theorems.
Received: 2008-04-18
Published Online: 2010-08-10
Published in Print: 2010-October
© de Gruyter 2010
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Artikel in diesem Heft
- A combinatorial approach to Alexander–Hirschowitz's Theorem based on toric degenerations
- Triply periodic minimal surfaces which converge to the Hoffman–Wohlgemuth example
- Total absolute horospherical curvature of submanifolds in hyperbolic space
- The case of equality for an inverse Santaló functional inequality
- Circle configurations in strictly convex normed planes
- Rank four vector bundles without theta divisor over a curve of genus two
- Affine Tallini Sets and Grassmannians
- Geometry of self-dual flats over a PID on a polarity
- Logarithmic comparison theorem versus Gauss–Manin system for isolated singularities
- A kinematic formula for the total absolute curvature of intersections
- Reducible Veronese surfaces
- Effective non-vanishing conjectures for projective threefolds
Schlagwörter für diesen Artikel
Hyperbolic space;
horospherical geometry;
the Chern–Lashof type inequality
Artikel in diesem Heft
- A combinatorial approach to Alexander–Hirschowitz's Theorem based on toric degenerations
- Triply periodic minimal surfaces which converge to the Hoffman–Wohlgemuth example
- Total absolute horospherical curvature of submanifolds in hyperbolic space
- The case of equality for an inverse Santaló functional inequality
- Circle configurations in strictly convex normed planes
- Rank four vector bundles without theta divisor over a curve of genus two
- Affine Tallini Sets and Grassmannians
- Geometry of self-dual flats over a PID on a polarity
- Logarithmic comparison theorem versus Gauss–Manin system for isolated singularities
- A kinematic formula for the total absolute curvature of intersections
- Reducible Veronese surfaces
- Effective non-vanishing conjectures for projective threefolds
