HORIZONTAL LAPLACE OPERATOR IN REAL FINSLER VECTOR BUNDLES

【摘要】 <正>A vector bundle F over the tangent bundle TM of a manifold M is said to be a Finsler vector bundle if it is isomorphic to the pull-backπ~*E of a vector bundle E over M([1]).In this article the authors study the h-Laplace operator in Finsler vector bundles. An h-Laplace operator is defined,first for functions and then for horizontal Finsler forms on E.Using the h-Laplace operator,the authors define the h-harmonic function and h- harmonic horizontal Finsler vector fields,and furthermore prove some integral formulas for the h-Laplace operator,horizontal Finsler vector fields,and scalar fields on E.更多还原

【Abstract】 A vector bundle F over the tangent bundle TM of a manifold M is said to be a Finsler vector bundle if it is isomorphic to the pull-backπ~*E of a vector bundle E over M([1]).In this article the authors study the h-Laplace operator in Finsler vector bundles. An h-Laplace operator is defined,first for functions and then for horizontal Finsler forms on E.Using the h-Laplace operator,the authors define the h-harmonic function and h- harmonic horizontal Finsler vector fields,and furthermore prove some integral formulas for the h-Laplace operator,horizontal Finsler vector fields,and scalar fields on E.更多还原