A Vanishing Cohomology Theorem of Nakano Type on Projectivized Finsler Bundle

[1] M. Abate and G. Patrizio, Finsler metrics-A global approach. Lectures Notes in Math., Springer-Verlag, Pisa, 199410.1007/BFb0073980Search in Google Scholar

[2] T. Aikou, A partial connection on complex Finsler bundles and its applications, Ilinois J. of Math., 42(3), (1998), 481-492.10.1215/ijm/1256044938Search in Google Scholar

[3] T. Aikou, Some remarks on projectively at complex Finsler metrics, Periodica Math. Hungarica, 48(1-2), (2004), 125-140.10.1023/B:MAHU.0000038970.83762.a7Search in Google Scholar

[4] T. Aikou, Finsler Geometry on Complex Vector Bundles, MSRI Publ., 50, (2004), 83-105.Search in Google Scholar

[5] T. Aikou, The Chern-Finsler connection and Finsler-Káhler manifolds, Adv. Stud. in Pure Math., 48, (2007), 343-373.Search in Google Scholar

[6] S. Bochner, Curvature in Hermitian metric, Bull. Amer. Math. Soc. Sci., 53, (1946), 179-195.10.1090/S0002-9904-1947-08778-4Search in Google Scholar

[7] S. Bochner, Vector fields and Ricci curvature, Bull. Amer. Math. Soc. Sci., 52, (1946), 776-797.10.1090/S0002-9904-1946-08647-4Search in Google Scholar

[8] S. Bochner, Tensor fields and Ricci curvature in Hermitian metric, Proc. Nat. Acad., 37, (1951), 704-706.10.1073/pnas.37.10.704106344916578405Search in Google Scholar

[9] J. K. Cao and P.-M. Wong, Finsler Geometry of Projectivized Vector Bundles, J. Math. Kyoto Univ., 43, (2003), 369-410.10.1215/kjm/1250283732Search in Google Scholar

[10] K. Chandler and P.-M. Wong, On the holomorphic sectional and bisectional curvatures in complex Finsler geometry, Periodica Math. Hungarica, 48(1-2), (2004), 93-123.10.1023/B:MAHU.0000038969.91179.e4Search in Google Scholar

[11] S. S. Chern, Complex manifolds, Chicago, 1956.Search in Google Scholar

[12] J Girbau, Vanishing cohomology theorems and stability of complex analytic foliations, Israel J. of Math., 40(3-4), (1981), 235-254.10.1007/BF02761365Search in Google Scholar

[13] J. Girbau, Pseudo-differential operators on V-manifolds and foliations: Part I, Col- lect. Math., 30, (1979), 247-265.Search in Google Scholar

[14] P. A. Griffiths, Hermitian di erential geometry, Chern classes and positive vector bundles, Princeton University Press, (1969), 185-252.10.1515/9781400871230-011Search in Google Scholar

[15] P. Griffiths and J. Harris, Principles of Algebraic Geometry, A Willey-Int. Publ., New York-Chichester-Brisbane-Toronto, 1978.Search in Google Scholar

[16] C. Ida, Vertical Laplacian on complex Finsler bundles, Acta Math. Acad. Paed. Nyiregyhaziensis, 26(2), (2010), 313-327.Search in Google Scholar

[17] C. Ida, A vanishing theorem for vertical tensor fields on complex Finsler bundles, An. St. Univ. "Al.I. Cuza", Iasi, 57, supplement, (2011), 103-112.10.2478/v10157-011-0006-3Search in Google Scholar

[18] C. Ida, A Nakano type inequality for mixed forms on complex Finsler manifolds, Mathematical Communications, 16(2), (2011), 471-479.Search in Google Scholar

[19] S. Kobayashi, Di erential Geometry of Complex Vector Bundles, Publ. of the Math. Soc. of Japan, Tokyo, 1987. 10.1515/9781400858682Search in Google Scholar