• Communications of the Korean Mathematical Society
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• v.38 no.1
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• pp.47-53
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• 2023

The Terracini t-locus of an embedded variety X ⊂ ℙ^r is the set of all cardinality t subsets of the smooth part of X at which a certain differential drops rank, i.e., the union of the associated double points is linearly dependent. We give an easy to check criterion to exclude some sets from the Terracini loci. This criterion applies to tensors and partially symmetric tensors. We discuss the non-existence of codimension 1 Terracini t-loci when t is the generic X-rank.

• Journal of the Korean Mathematical Society
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• v.42 no.3
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• pp.435-445
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• 2005

The purpose of this paper is to study a Kenmotsu manifold which is derived from the almost contact Riemannian manifold with some special conditions. In general, we have some relations about semi-symmetric, Ricci semi-symmetric or Weyl semisymmetric conditions in Riemannian manifolds. In this paper, we partially classify the Kenmotsu manifold and consider the manifold admitting a transformation which keeps Riemannian curvature tensor and Ricci tensor invariant.