Unit tangent sphere bundles with constant scalar curvature

Eric Boeckx; Lieven Vanhecke

Czechoslovak Mathematical Journal (2001)

  • Volume: 51, Issue: 3, page 523-544
  • ISSN: 0011-4642

Abstract

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As a first step in the search for curvature homogeneous unit tangent sphere bundles we derive necessary and sufficient conditions for a manifold to have a unit tangent sphere bundle with constant scalar curvature. We give complete classifications for low dimensions and for conformally flat manifolds. Further, we determine when the unit tangent sphere bundle is Einstein or Ricci-parallel.

How to cite

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Boeckx, Eric, and Vanhecke, Lieven. "Unit tangent sphere bundles with constant scalar curvature." Czechoslovak Mathematical Journal 51.3 (2001): 523-544. <http://eudml.org/doc/30653>.

@article{Boeckx2001,
abstract = {As a first step in the search for curvature homogeneous unit tangent sphere bundles we derive necessary and sufficient conditions for a manifold to have a unit tangent sphere bundle with constant scalar curvature. We give complete classifications for low dimensions and for conformally flat manifolds. Further, we determine when the unit tangent sphere bundle is Einstein or Ricci-parallel.},
author = {Boeckx, Eric, Vanhecke, Lieven},
journal = {Czechoslovak Mathematical Journal},
keywords = {unit tangent sphere bundles; constant scalar curvature; Einstein and Ricci-parallel metrics; unit tangent sphere bundles; constant scalar curvature; Einstein and Ricci-parallel metrics},
language = {eng},
number = {3},
pages = {523-544},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Unit tangent sphere bundles with constant scalar curvature},
url = {http://eudml.org/doc/30653},
volume = {51},
year = {2001},
}

TY - JOUR
AU - Boeckx, Eric
AU - Vanhecke, Lieven
TI - Unit tangent sphere bundles with constant scalar curvature
JO - Czechoslovak Mathematical Journal
PY - 2001
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 51
IS - 3
SP - 523
EP - 544
AB - As a first step in the search for curvature homogeneous unit tangent sphere bundles we derive necessary and sufficient conditions for a manifold to have a unit tangent sphere bundle with constant scalar curvature. We give complete classifications for low dimensions and for conformally flat manifolds. Further, we determine when the unit tangent sphere bundle is Einstein or Ricci-parallel.
LA - eng
KW - unit tangent sphere bundles; constant scalar curvature; Einstein and Ricci-parallel metrics; unit tangent sphere bundles; constant scalar curvature; Einstein and Ricci-parallel metrics
UR - http://eudml.org/doc/30653
ER -

References

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