A new characterization of Finsler metrics with constant flag curvature 1
Xiaohuan MO
A new characterization of Finsler metrics with constant flag curvature 1
The purpose of this article is to derive an integral inequality of Ricci curvature with respect to Reeb field in a Finsler space and give a new geometric characterization of Finsler metrics with constant flag curvature 1.
Finsler metric / constant flag curvature / Reeb vector field
[1] |
Bao D, Chern S S, Shen Z. On the Gauss-Bonnet integrand for 4-dimensional Landsberg spaces. In: Bao D, Chern S S, Shen Z, eds. Finsler Geometry, Joint summer Research Conference on Finsler Geometry, July 16–20, 1995, Seattle, Washington. Contemp Math, 196. Providence: Amer Math Soc, 1996, 15-25
|
[2] |
Bao D, Chern S-S, Shen Z. An Introduction to Riemann-Finsler Geometry. Graduate Texts in Mathematics, 200. New York: Springer-Verlag, 2000
|
[3] |
Bao D, Robles C, Shen Z. Zermelo navigation on Riemannian manifolds. J Differential Geom, 2004, 66: 377-435
|
[4] |
Bao D, Shen Z. On the volume of unit tangent spheres in a Finsler manifold. Results Math, 1994, 26: 1-17
|
[5] |
Bao D, Shen Z. Finsler metrics of constant positive curvature on the Lie group S3. J London Math Soc, 2002, 66(2): 453-467
CrossRef
Google scholar
|
[6] |
Bejancu A, Farran H R. A geometric characterization of Finsler manifolds of constant curvature K = 1. Inter J Math and Math Sci, 2000, 23: 399-407
CrossRef
Google scholar
|
[7] |
Bryant R L. Finsler structures on the 2-sphere satisfying K = 1. In: Bao D, Chern S S, Shen Z, eds. Finsler Geometry, Joint summer Research Conference on Finsler Geometry, July 16–20, 1995, Seattle, Washington. Contemp Math, 196. Providence: Amer Math Soc, 1996, 27-41
|
[8] |
Bryant R L. Projectively flat Finsler 2-spheres of constant curvature. Selecta Math (NS), 1997, 3: 161-203
CrossRef
Google scholar
|
[9] |
Bryant R L. Some remarks on Finsler manifolds with constant flag curvature. Special Issue for S. S. Chern. Houston J Math, 2002, 28: 221-262
|
[10] |
Chern S S. Riemannian geometry as a special case of Finsler geometry. Contem Math, 1996, 196: 51-58
|
[11] |
Chern S S, Carmo M do, Kobayashi S. Minimal submanifolds of a sphere with second fundamental form of constant length. In: Browder F E, ed. Functional Analysis and Related Fields. Berlin: Springer-Verlag, 1970, 59-75
|
[12] |
Chern S S, Shen Z. Riemann-Finsler Geometry. Nankai Tracts in Mathematics, 6. Hackensack: World Scientific Publishing Co Pte Ltd, 2005
|
[13] |
Li A, Li J. An intrinsic rigidity theorem for minimal submanifolds in a sphere. Arch Math (Basel), 1992, 58: 582-594
|
[14] |
Mo X. Characterization and structure of Finsler spaces with constant flag curvature. Sci China, Ser A, 1998, 41: 910-917
CrossRef
Google scholar
|
[15] |
Mo X. Flag curvature tensor on a closed Finsler surface. Result in Math, 1999, 36: 149-159
|
[16] |
Mo X. On the flag curvature of a Finsler space with constant S-curvature. Houston Journal of Mathematics, 2005, 31: 131-144
|
[17] |
Mo X. An Introduction to Finsler Geometry. Singapore: World Scientific Press, 2006
CrossRef
Google scholar
|
[18] |
Mo X, Yu C. On the Ricci curvature of a Randers metrics of isotropic S-curvature. Acta Mathematica Sinica (NS), 2008, 24: 991-996
|
[19] |
Peng C, Terng C. The scalar curvature of minimal hypersurfaces in spheres. Math Ann, 1983, 266: 105-113
CrossRef
Google scholar
|
[20] |
Shen Y. On intrinsic rigidity for minimal submanifolds in a sphere. Sci China, Ser A, 1989, 32: 769-781
|
[21] |
Shen Z. Projectively flat Finsler metrics of constant flag curvature. Trans Amer Math Soc, 2003, 355: 1713-1728
CrossRef
Google scholar
|
[22] |
Simons J. Minimal varieties in Riemannian manifolds. Ann Math, 1968, 83: 62-105
CrossRef
Google scholar
|
[23] |
Yano K. On harmonic and Killing vector fields. Ann Math, 1952, 55: 38-45
CrossRef
Google scholar
|
[24] |
Yano K. Integral Formulas in Riemannian Geometry. Pure and Applied Mathematics, No 1. New York: Marcel Dekker, Inc, 1970
|
/
〈 | 〉 |