On Submanifolds with 2-Type Pseudo-Hyperbolic Gauss Map in Pseudo-Hyperbolic Space
Sign Up to like & getrecommendations! Published in 2017 at "Mediterranean Journal of Mathematics"
DOI: 10.1007/s00009-016-0819-0
Abstract: In this paper, we study pseudo-Riemannian submanifolds of a pseudo-hyperbolic space $$\mathbb H^{m-1}_s (-1) \subset \mathbb E^m_{s+1}$$Hsm-1(-1)⊂Es+1m with 2-type pseudo-hyperbolic Gauss map. We give a characterization of proper pseudo-Riemannian hypersurfaces in $$\mathbb H^{n+1}_s (-1) \subset… read more here.
Keywords: pseudo hyperbolic; type pseudo; mathbb; hyperbolic gauss ... See more keywords
Invariant surfaces with coordinate finite-type Gauss map in simply isotropic space
Sign Up to like & getrecommendations! Published in 2020 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2020.124673
Abstract: Abstract We consider the extrinsic geometry of surfaces in simply isotropic space, a three-dimensional space equipped with a rank 2 metric of index zero. Since the metric is degenerate, a surface normal cannot be unequivocally… read more here.
Keywords: simply isotropic; isotropic space; invariant surfaces; map ... See more keywords
Gauss Map Based Curved Origami Discretization
Sign Up to like & getrecommendations! Published in 2018 at "Journal of Mechanisms and Robotics"
DOI: 10.1115/1.4041631
Abstract: This paper addresses the problem of discretizing the curved developable surfaces that are satisfying the equivalent surface curvature change discretizations. Solving basic folding units occurs in such tasks as simulating the behavior of Gauss mapping.… read more here.
Keywords: discretization; gauss; curved surface; developable surfaces ... See more keywords
Extension of eigenvalue problems on Gauss map of ruled surfaces
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DOI: 10.20944/preprints201809.0407.v1
Abstract: A finite-type immersion or smooth map is a nice tool to classify submanifolds of Euclidean space, which comes from eigenvalue problem of immersion. The notion of generalized 1-type is a natural generalization of those of… read more here.
Keywords: extension eigenvalue; problems gauss; eigenvalue problems; type ... See more keywords
Classification Theorems of Ruled Surfaces in Minkowski Three-Space
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DOI: 10.3390/math6120318
Abstract: By generalizing the notion of the pointwise 1-type Gauss map, the generalized 1-type Gauss map has been recently introduced. Without any assumption, we classified all possible ruled surfaces with the generalized 1-type Gauss map in… read more here.
Keywords: generalized type; space; type gauss; ruled surfaces ... See more keywords