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J. Korean Math. Soc. 1998; 35(4): 831-841

Printed December 1, 1998

Copyright © The Korean Mathematical Society.

Notes on vanishing theorems on Riemannian manifolds with boundary

Haruo Kitahara and Hong Kyung Pak

Kanazawa University and Kyungsan University

Abstract

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We shall discuss on some vanishing theorems of harmonic sections of a Riemannian vector bundle over a compact Riemannian manifold with boundary. In relating the results of H. Donnelly - P. Li ([4]), for special case of harmonic forms satisfying absolute or relative boundary problem, our results improve the vanishing results of T. Takahashi ([9]).

Keywords: harmonic section, absolute or relative boundary problem, Kato inequality, vanishing

MSC numbers: 53C20

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