Soldered tensor fields of normalized submanifolds

Details Soldered tensor fields of normalized submanifolds Soldered tensor fields of normalized submanifolds

2010-06-30

arxiv.org/abs/1006.5792v1

Libertas Mathematica, 30 (2010), 39-46

Mathematics

Differential Geometry

LaTeX, 8 pages

Scientific paper

In an earlier paper we discussed soldered forms, multivector fields and Riemannian metrics. In particular, we showed that a Riemannian submanifold is totally geodesic iff the metric is soldered to the submanifold. In the present note we discuss general, soldered tensor fields. In particular, we prove that the almost complex structure of an almost K\"ahler manifold is soldered to a submanifold iff the latter is an invariant, totally geodesic submanifold.

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