Laplace Operators in Differential Geometry
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In differential geometry there are a number of second-order, linear, elliptic differential operators bearing the name Laplacian. This article provides an overview of some of them.The connection Laplacian is a differential operator acting on the various tensor bundles of a manifold, defined in terms of a Riemannian- or pseudo-Riemannian metric. When applied to functions (i.e, tensors of rank 0), the connection Laplacian is often called the Laplace Beltrami operator. On…mehr

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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In differential geometry there are a number of second-order, linear, elliptic differential operators bearing the name Laplacian. This article provides an overview of some of them.The connection Laplacian is a differential operator acting on the various tensor bundles of a manifold, defined in terms of a Riemannian- or pseudo-Riemannian metric. When applied to functions (i.e, tensors of rank 0), the connection Laplacian is often called the Laplace Beltrami operator. On a Riemannian manifold, one can define the conformal Laplacian as an operator on smooth functions; it differs from the Laplace Beltrami operator by a term involving the scalar curvature of the underlying metric.