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We first extend the notions of weighted curvatures, includ- ing the weighted flag curvature and the weighted Ricci curvature, for a Finsler manifold with given volume form. Then we establish some basic comparison theorems for Finsler manifolds with various weighted curva- ture bounds. As applications, we obtain some McKean type theorems for the first eigenvalue of Finsler manifolds, some results on weighted curva- ture and fundamental group for Finsler manifolds, as well as an estimation of Gromov simplicial norms for reversible Finsler manifolds.
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참고문헌 (19)
참고문헌 신청
B. Y. Wu / 2007 / Comparison theorems in Finsler geometry and their applica-tions / Math. Ann 337 (1) : 177 ~ 196
B. Y. Wu / 2011 / Volume form and its applications in Finsler geometry / Publ. Math. Debrecen 78 (3-4) : 723 ~ 741
B. Y. Wu / 2013 / Some results on curvature and topology of Finsler manifolds / Ann. Polon. Math 107 (3) : 309 ~ 320
D. Bao / 2000 / An introduction to Riemann-Finsler Geometry / GTM 200
E. Calabi / 1975 / On manifolds with nonnegative Ricci curvature II / Notices Amer. Math. Soc 22
B. Y. Wu / 2011 / Volume form and its applications in Finsler geometry / Publ. Math. Debrecen 78 (3-4) : 723 ~ 741
B. Y. Wu / 2013 / Some results on curvature and topology of Finsler manifolds / Ann. Polon. Math 107 (3) : 309 ~ 320
D. Bao / 2000 / An introduction to Riemann-Finsler Geometry / GTM 200
E. Calabi / 1975 / On manifolds with nonnegative Ricci curvature II / Notices Amer. Math. Soc 22
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