Quasi-Positive Curvature on Homogeneous Bundles

Type: Article

Publication Date: 2003-10-01

Citations: 32

DOI: https://doi.org/10.4310/jdg/1090511688

Abstract

We provide new examples of manifolds which admit a Riemannian metric with sectional curvature nonnegative, and strictly positive at one point. Our examples include the unit tangent bundles of ℂℙn, ℍℙn and \mathbb Oℙn (the Cayley plane), and a family of lens space bundles over ℂℙn.

Locations

  • Journal of Differential Geometry - View - PDF
  • arXiv (Cornell University) - View - PDF

Similar Works

Action Title Year Authors
+ Quasi-positive curvature on homogeneous bundles 2003 Kristopher Tapp
+ Riemannian manifolds of quasi-constant sectional curvatures 2000 Georgi Ganchev
Vesselka Mihova
+ Homogeneous riemannian manifolds of non-positive sectional curvature 1963 Róbert Hermann
+ Can tangent sphere bundles over Riemannian manifolds have strictly positive sectional curvature? 2001 O. Kowalski
M. Sekizawa
Z. Vlášek
+ Quasi-negative holomorphic sectional curvature and positivity of the canonical bundle 2016 Simone Diverio
Stefano Trapani
+ Kahler structures on the tangent bundle of Riemannianmanifolds of constant positive curvature 1999 Kiyotaka Ii
Tsuyoshi Morikawa
+ Quasi-negative holomorphic sectional curvature and positivity of the canonical bundle 2016 Simone Diverio
Stefano Trapani
+ Riemannian Manifolds with positive sectional curvature 2012 Wolfgang Ziller
+ Obstructions to Positive Curvature on Homogeneous Bundles 2005 Kristopher Tapp
+ The Geometry of Curvature Homogeneous Pseudo-Riemannian Manifolds 2007 Peter Gilkey
+ Riemannian geometry as a curved pre-homogeneous geometry 2010 Ercüment H. Ortaçgil
+ Curvature homogeneous unit tangent sphere bundles 1998 Eric Boeckx
L. Vanhecke
+ Compact Homogeneous Riemannian Manifolds with Strictly Positive Curvature 1972 Nolan R. Wallach
+ A flat pseudo-Riemannian structure on the tangent bundle of a flat manifold 1992 V. V. Trofimov
+ The structure of manifolds of nonnegative sectional curvature 2007 Christy Cameron
+ Metrics with nonnegative isotropic curvature 1993 Mario Micallef
McKenzie Y. Wang
+ Submanifolds of constant sectional curvature in Pseudo-Riemannian manifolds 1996 Jo�o Lucas Barbosa
Walterson Ferreira
Keti Tenenblat
+ PDF Chat Obstruction to Positive Curvature on Homogeneous Bundles 2006 Kristopher Tapp
+ PDF Chat Homogeneous Riemannian manifolds of negative curvature 1962 Shôshichi Kobayashi
+ Invariant metrics of positive Ricci curvature on principal bundles 1998 Peter Gilkey
JeongHyeong Park
Wilderich Tuschmann

Works That Cite This (32)

Action Title Year Authors
+ PDF Chat The classification of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mrow><mml:mi mathvariant="italic">SU</mml:mi></mml:mrow><mml:msup><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mn>2</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:math> biquotients of rank 3 Lie groups 2015 Jason DeVito
Robert DeYeso
+ PDF Chat The classification and curvature of biquotients of the form $$Sp(3)/\!\!/Sp(1)^2$$ S p ( 3 ) / / S p ( 1 ) 2 2014 Jason DeVito
Robert DeYeso
Michael Ruddy
Philip Wesner
+ PDF Chat Some new examples with almost positive curvature 2011 Martin Kerin
+ PDF Chat A Note on Maximal Symmetry Rank, Quasipositive Curvature, and Low Dimensional Manifolds 2014 Fernando Galaz‐García
+ Orbifold biquotients of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mrow><mml:mi mathvariant="italic">SU</mml:mi></mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mn>3</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math> 2015 Dmytro Yeroshkin
+ PDF Chat The classification of compact simply connected biquotients in dimension 6 and 7 2016 Jason DeVito
+ PDF Chat Topological obstructions to fatness 2011 Luis A. Florit
Wolfgang Ziller
+ PDF Chat Examples of Manifolds with Non-negative Sectional Curvature 2006 Wolfgang Ziller
+ PDF Chat Rationally 4-periodic biquotients 2017 Jason DeVito
+ Infinite families of manifolds of positive $k^{\rm th}$-intermediate Ricci curvature with $k$ small 2020 Miguel Domínguez-Vázquez
David González-Álvaro
Lawrence Mouillé