A curvature identity on a 6-dimensional Riemannian manifold and its applications

Yunhee Euh; Jeong Hyeong Park; Kouei Sekigawa

Czechoslovak Mathematical Journal (2017)

  • Volume: 67, Issue: 1, page 253-270
  • ISSN: 0011-4642

Abstract

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We derive a curvature identity that holds on any 6-dimensional Riemannian manifold, from the Chern-Gauss-Bonnet theorem for a 6-dimensional closed Riemannian manifold. Moreover, some applications of the curvature identity are given. We also define a generalization of harmonic manifolds to study the Lichnerowicz conjecture for a harmonic manifold “a harmonic manifold is locally symmetric” and provide another proof of the Lichnerowicz conjecture refined by Ledger for the 4-dimensional case under a slightly more general setting.

How to cite

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Euh, Yunhee, Park, Jeong Hyeong, and Sekigawa, Kouei. "A curvature identity on a 6-dimensional Riemannian manifold and its applications." Czechoslovak Mathematical Journal 67.1 (2017): 253-270. <http://eudml.org/doc/287904>.

@article{Euh2017,
abstract = {We derive a curvature identity that holds on any 6-dimensional Riemannian manifold, from the Chern-Gauss-Bonnet theorem for a 6-dimensional closed Riemannian manifold. Moreover, some applications of the curvature identity are given. We also define a generalization of harmonic manifolds to study the Lichnerowicz conjecture for a harmonic manifold “a harmonic manifold is locally symmetric” and provide another proof of the Lichnerowicz conjecture refined by Ledger for the 4-dimensional case under a slightly more general setting.},
author = {Euh, Yunhee, Park, Jeong Hyeong, Sekigawa, Kouei},
journal = {Czechoslovak Mathematical Journal},
keywords = {Chern-Gauss-Bonnet theorem; curvature identity; locally harmonic manifold; Einstein manifold; Singer-Thorpe basis; Hitchin inequality},
language = {eng},
number = {1},
pages = {253-270},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A curvature identity on a 6-dimensional Riemannian manifold and its applications},
url = {http://eudml.org/doc/287904},
volume = {67},
year = {2017},
}

TY - JOUR
AU - Euh, Yunhee
AU - Park, Jeong Hyeong
AU - Sekigawa, Kouei
TI - A curvature identity on a 6-dimensional Riemannian manifold and its applications
JO - Czechoslovak Mathematical Journal
PY - 2017
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 67
IS - 1
SP - 253
EP - 270
AB - We derive a curvature identity that holds on any 6-dimensional Riemannian manifold, from the Chern-Gauss-Bonnet theorem for a 6-dimensional closed Riemannian manifold. Moreover, some applications of the curvature identity are given. We also define a generalization of harmonic manifolds to study the Lichnerowicz conjecture for a harmonic manifold “a harmonic manifold is locally symmetric” and provide another proof of the Lichnerowicz conjecture refined by Ledger for the 4-dimensional case under a slightly more general setting.
LA - eng
KW - Chern-Gauss-Bonnet theorem; curvature identity; locally harmonic manifold; Einstein manifold; Singer-Thorpe basis; Hitchin inequality
UR - http://eudml.org/doc/287904
ER -

References

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