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The extrinsic holonomy Lie algebra of a parallel submanifold | Tillmann Jentsch
; | Date: |
17 Apr 2009 | Abstract: | We investigate parallel submanifolds in a Riemannian symmetric space $N$. The
special case of a symmetric submanifold has been investigated by many authors
before and is well understood. We observe that there exists an intrinsic
property of the second fundamental form which distinguishes full symmetric
submanifolds from arbitrary full parallel submanifolds of $N$. Furthermore, for
a submanifold $M$ of $N$ we consider the holonomy Lie algebra of the pullback
bundle $TN|M$. If $M$ is a full parallel submanifold of $N$, then we are able
to describe the general structure of this Lie algebra. If moreover $N$ is
simply connected and $M$ is even a full symmetric submanifold of $N$, then we
are able to calculate the holonomy Lie algebra of $TN|M$ in an explicit form. | Source: | arXiv, 0904.2611 | Services: | Forum | Review | PDF | Favorites |
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