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Tensor product surfaces of euclidean plane curves
Ion Mihai,Bernard Rouxel +1 more
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In this paper, the authors studied the tensor product of two Euclidean plane curves and established necessary and sufficient conditions for such a product to be totally real or complex or slant.Abstract:
Recently B.Y. CHEN initiated the study of the tensor product immersion of two immersions of a given Riemannian manifold [3]. In [6] the particular case of tensor product of two Euclidean plane curves was studied. The minimal one were classified, and necessary and sufficient conditions for such a tensor product to be totally real or complex or slant were established. In the present paper we study for tensor product of Euclidean plane curves the problem of B.Y. CHEN: to what extent do the properties of the tensor product immersion f ⊗ h of two immersions f, h determines the immersions f, h ? [3]read more
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Lagrangian isometric immersions of a real-space-form M n ( c ) into a complex-space-form M ˜ n (4 c )
TL;DR: In this paper, it was shown that a twisted product decomposition of a real-space-form of the form f1 I1 fk Ik 1 N n k (c) admits a unique adapted Lagrangian isometric immersion into a complex-space form f M n (4c) of constant holomorphic sectional curvature 4c.
Journal ArticleDOI
Tensor product surfaces with pointwise 1-type gauss map
TL;DR: In this article, Chen et al. studied the tensor product surfaces of two Euclidean plane curves and gave necessary and sufficient conditions for such surfaces to have pointwise 1-type Gauss maps.
Journal Article
Special proper pointwise slant surfaces of a locally product Riemannian manifold
TL;DR: In this article, the structure of pointwise slant submanifolds in an almost product Riemannian manifold is investigated and the special proper pointwise-slant surfaces of a locally product manifold are introduced.
Journal ArticleDOI
Vranceanu surface in \( \mathbb{E}^4 \) with pointwise 1- type Gauss map
TL;DR: In this paper, the authors investigated Vranceanu rotation surfaces with pointwise 1-type Gauss map in Euclidean 4-space and gave necessary and sufficent conditions for such surfaces to have pointwise Gauss maps.
An inequality for totally real surfaces in complex space forms
TL;DR: For a Lagrangian surface M of a complex space form f M(4c) of arbitrary codimen-sion, the authors obtained an inequality relating the squared mean curvature kHk 2, the holomorphic sectional curvature c, the Gauss curvature K and the elliptic curvature E of the surface.
References
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$A$-submanifolds in Euclidean space
TL;DR: In this paper, a geometrical characterization of v4-submanifolds M of a Euclidean space E using the (p-2)th polar hypersurface KTM of the characteristic hypersurf ace K of the normal space T^M, m^M.
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