Some rigidity theorems for Finsler manifolds of sectional flag curvature

Bing Ye Wu

Archivum Mathematicum (2010)

  • Volume: 046, Issue: 2, page 99-104
  • ISSN: 0044-8753

Abstract

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In this paper we study some rigidity properties for Finsler manifolds of sectional flag curvature. We prove that any Landsberg manifold of non-zero sectional flag curvature and any closed Finsler manifold of negative sectional flag curvature must be Riemannian.

How to cite

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Wu, Bing Ye. "Some rigidity theorems for Finsler manifolds of sectional flag curvature." Archivum Mathematicum 046.2 (2010): 99-104. <http://eudml.org/doc/37770>.

@article{Wu2010,
abstract = {In this paper we study some rigidity properties for Finsler manifolds of sectional flag curvature. We prove that any Landsberg manifold of non-zero sectional flag curvature and any closed Finsler manifold of negative sectional flag curvature must be Riemannian.},
author = {Wu, Bing Ye},
journal = {Archivum Mathematicum},
keywords = {Finsler manifold; Landsberg manifold; scalar flag curvature; sectional flag curvature; Cartan tensor; Finsler manifold; Landsberg manifold; scalar flag curvature; sectional flag curvature; Cartan tensor},
language = {eng},
number = {2},
pages = {99-104},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Some rigidity theorems for Finsler manifolds of sectional flag curvature},
url = {http://eudml.org/doc/37770},
volume = {046},
year = {2010},
}

TY - JOUR
AU - Wu, Bing Ye
TI - Some rigidity theorems for Finsler manifolds of sectional flag curvature
JO - Archivum Mathematicum
PY - 2010
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 046
IS - 2
SP - 99
EP - 104
AB - In this paper we study some rigidity properties for Finsler manifolds of sectional flag curvature. We prove that any Landsberg manifold of non-zero sectional flag curvature and any closed Finsler manifold of negative sectional flag curvature must be Riemannian.
LA - eng
KW - Finsler manifold; Landsberg manifold; scalar flag curvature; sectional flag curvature; Cartan tensor; Finsler manifold; Landsberg manifold; scalar flag curvature; sectional flag curvature; Cartan tensor
UR - http://eudml.org/doc/37770
ER -

References

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  1. Akbar-Zadeh, H., Sur les espaces de Finsler à courbures sectionnelles constantes, Acad. Roy. Belg. Bull. Cl. Sci. (6) 74 (1988), 281–322. (1988) Zbl0686.53020MR1052466
  2. Chen, B., Zhao, L. L., Randers metrics of sectional flag curvature, Houston J. Math., to appear. MR2610781
  3. Chen, X., Mo, X., Shen, Z., 10.1112/S0024610703004599, J. London Math. Soc. 68 (2003), 762–780. (2003) Zbl1063.53078MR2010010DOI10.1112/S0024610703004599
  4. Chern, S. S., Local equivalence and Euclidean connections in Finsler spaces, Sci. Rep. Nat. Tsing Hua Univ. Ser. A5 (1948), 95–121, or Selected Papers, II, 194-212, Springer 1989. (1948) Zbl0200.00004MR0031812
  5. Chern, S. S., Shen, Z., Riemannian-Finsler geometry, World Sci., Singapore, 2005. (2005) MR2169595
  6. Mo, X., 10.1007/BF03322108, Res. Math. 36 (1999), 149–159. (1999) MR1706528DOI10.1007/BF03322108
  7. Numata, S., On Landsberg spaces of scalar curvature, J. Korean Math. Soc. 12 (1975), 97–100. (1975) Zbl0314.53017MR0402643

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