<abstract xmlns="http://www.w3.org/1999/xhtml"><p> It is well known that a complex Finsler structure F on a holomorphic vector bundle E over a compact Kähler manifold (M; g) defines a bundle-like pseudo-Kähler metric of Sasaki type on the total space of the associated projectivized bundle PE. Then using an argument inspired from the theory of vanishing theorems for complex analytic foliations, we obtain a vanishing cohomology theorem of Nakano's type for base-like forms with values in a foliated line bundle over PE. </p></abstract>

It is well known that a complex Finsler structure F on a holomorphic vector bundle E over a compact Kähler manifold (M; g) defines a bundle-like pseudo-Kähler metric of Sasaki type on the total space of the associated projectivized bundle PE. Then using an argument inspired from the theory of vanishing theorems for complex analytic foliations, we obtain a vanishing cohomology theorem of Nakano's type for base-like forms with values in a foliated line bundle over PE.

A Vanishing Cohomology Theorem of Nakano Type on Projectivized Finsler Bundle

Department of Mathematics and Informatics "Transilvania" University of Braşov, Iuliu Maniu street nr. 50, 500091 Braşov

Annals of West University of Timisoara - Mathematics and Computer Science

{"article-title":"A Vanishing Cohomology Theorem of Nakano Type on Projectivized Finsler Bundle"}

It is well known that a complex Finsler structure F on a holomorphic vector bundle E over a compact Kähler manifold (M; g) defines a bundle-like pseudo-Kähler...

A Vanishing Cohomology Theorem of Nakano Type on Projectivized Finsler Bundle

Published Online: Aug 14, 2013

Page range: 63 - 73

DOI: https://doi.org/10.2478/awutm-2013-0005

Keywords
complex Finsler structure, vanishing theorem

This content is open access.

A Vanishing Cohomology Theorem of Nakano Type on Projectivized Finsler Bundle

Published Online: Aug 14, 2013

Page range: 63 - 73

DOI: https://doi.org/10.2478/awutm-2013-0005

Keywordscomplex Finsler structure, vanishing theorem

This content is open access.

Keywords
complex Finsler structure, vanishing theorem