Geodesic
Horizontal Forms of Chern Type on Complex Finsler Bundles
Symmetry, integrability and geometry: methods and applications, Tome 6 (2010) Cet article a éte moissonné depuis la source Math-Net.Ru

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The aim of this paper is to construct horizontal Chern forms of a holomorphic vector bundle using complex Finsler structures. Also, some properties of these forms are studied.
Keywords: complex Finsler bundles; horizontal forms of Chern type. 
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     author = {Cristian Ida},
     title = {Horizontal {Forms} of {Chern} {Type} on {Complex} {Finsler} {Bundles}},
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     volume = {6},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2010_6_a53/}
}
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Cristian Ida. Horizontal Forms of Chern Type on Complex Finsler Bundles. Symmetry, integrability and geometry: methods and applications, Tome 6 (2010). http://geodesic.mathdoc.fr/item/SIGMA_2010_6_a53/

[1] Abate M., Patrizio G., Finsler metrics – a global approach. With applications to geometric function theory, Lectures Notes in Math., 1591, Springer-Verlag, Berlin, 1994 | MR | Zbl

[2] Aikou T., “A note on infinitesimal deformations of complex Finsler structures”, An. Ştiinţ. Univ. Al. I. Cuza Iaşi. Mat. (N.S.), 43 (1997), 295–305 | MR | Zbl

[3] Aikou T., “Applications of Bott connection to Finsler geometry”, Proceedings of the Colloquium “Steps in Differential Geometry” (Debrecen, 2000), Inst. Math. Inform., Debrecen, 2001, 1–13 | MR | Zbl

[4] Aikou T., “Finsler geometry on complex vector bundles”, A sampler of Riemann–Finsler geometry, Math. Sci. Res. Inst. Publ., 50, Cambridge Univ. Press, Cambridge, 2004, 83–105 | MR | Zbl

[5] Cao J.-K., Wong P.-M., “Finsler geometry of projectivized vector bundles”, J. Math. Kyoto Univ., 43 (2003), 369–410 | MR | Zbl

[6] Chandler K., Wong P.-M., “On the holomorphic sectional and bisectional curvatures in complex Finsler geometry”, Period. Math. Hungar., 48 (2004), 93–123 | DOI | MR | Zbl

[7] Faran J. J., “The equivalence problem for complex Finsler Hamiltonians”, Finsler Geometry (Seattle, WA, 1995), Contemp. Math., 196, Amer. Math. Soc., Providence, RI, 1996, 133–144 | MR | Zbl

[8] Griffiths P., Harris J., Principles of algebraic geometry, Pure and Applied Mathematics, Wiley-Interscience, New York, 1978 | MR | Zbl

[9] Kobayashi S., “Negative vector bundles and complex Finsler structures”, Nagoya Math. J., 57 (1975), 153–166 http://projecteuclid.org/getRecord?id=euclid.nmj/1118795367 | MR | Zbl

[10] Kobayashi S., “Differential geometry of complex vector bundles”, Publications of the Mathematical Society of Japan, v. 5, Kanô Memorial Lectures, 15, Princeton University Press, Princeton, NJ; Iwanami Shoten, Tokyo, 1987 | MR | Zbl

[11] Kobayashi S., “Complex Finsler vector bundles”, Finsler Geometry (Seattle, WA, 1995), Contemp. Math., 196, Amer. Math. Soc., Providence, RI, 1996, 145–153 | MR | Zbl

[12] Munteanu G., Complex spaces in Finsler, Lagrange and Hamilton geometries, Fundamental Theories of Physics, 141, Kluwer Academic Publishers, Dordrecht, 2004 | MR | Zbl

[13] Pitis G., Munteanu G., “$V$-cohomology of complex Finsler manifolds”, Studia Univ. Babeş-Bolyai Math., 43:3 (1998), 75–82 | MR | Zbl

[14] Rund H., “Generalized metrics on complex manifolds”, Math. Nachr., 34 (1967), 55–77 | DOI | MR | Zbl

[15] Vaisman I., Cohomology and differential forms, Pure and Applied Mathematics, 21, Marcel Dekker, Inc., New York, 1973 | MR | Zbl

[16] Wong P. M., “A survey of complex Finsler geometry”, Finsler Geometry, Sapporo 2005 – in Memory of Makoto Matsumoto, Adv. Stud. Pure Math., 48, Math. Soc. Japan, Tokyo, 2007, 375–433 | MR | Zbl

[17] Zhong C., Zhong T., “Horizontal $\overline\partial$-Laplacian on complex Finsler manifolds”, Sci. China Ser. A, 48, suppl. (2005), 377–391 | DOI | MR | Zbl

[18] Zhong C., Zhong T., “Hodge decomposition theorem on strongly Kähler Finsler manifolds”, Sci. China Ser. A, 49 (2006), 1696–1714 | DOI | MR | Zbl