English

Soldered tensor fields of normalized submanifolds

Differential Geometry 2010-07-01 v1

Abstract

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.

Keywords

Cite

@article{arxiv.1006.5792,
  title  = {Soldered tensor fields of normalized submanifolds},
  author = {Izu Vaisman},
  journal= {arXiv preprint arXiv:1006.5792},
  year   = {2010}
}

Comments

LaTeX, 8 pages

R2 v1 2026-06-21T15:42:47.843Z