• Journal of the Korean Mathematical Society
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• v.34 no.2
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• pp.437-452
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• 1997

We study low type submanifolds in pseudo-Euclidean space which is especially of 2-type pseudo-umbilical. We also determine full null 2-type surfaces with parallel mean curvature vector in 4-dimensional Minkowski space-time.

• Communications of the Korean Mathematical Society
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• v.34 no.3
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• pp.935-949
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• 2019

The purpose of the paper is to study the notion of pseudo-slant submanifolds and the existence of some structures on a pseudo-slant submanifolds of nearly (${\varepsilon},{\delta}$)-trans-Sasakian manifold. Totally umbilical proper-slant submanifolds are worked out. We discuss the integrability of distributions on pseudo-slant submanifolds of nearly (${\varepsilon},{\delta}$)-trans-Sasakian manifold.

• Bulletin of the Korean Mathematical Society
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• v.55 no.6
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• pp.1823-1834
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• 2018

The position vector field x is the most elementary and natural geometric object on a Euclidean submanifold M. The position vector field plays very important roles in mathematics as well as in physics. Similarly, the tangential component $x^T$ of the position vector field is the most natural vector field tangent to the Euclidean submanifold M. We simply call the vector field $x^T$ the canonical vector field of the Euclidean submanifold M. In earlier articles [4,5,9,11,12], we investigated Euclidean submanifolds whose canonical vector fields are concurrent, concircular, torse-forming, conservative or incompressible. In this article we study Euclidean submanifolds with conformal canonical vector field. In particular, we characterize such submanifolds. Several applications are also given. In the last section we present three global results on complete Euclidean submanifolds with conformal canonical vector field.