Abstract
In this paper, by taking into account the beginning of the hypersurface theory in Euclidean space $E^4$, a practical method for the matrix of the Weingarten map (or the shape operator) of an oriented hypersurface $M^3$ in $E^4$ is obtained. By taking this efficient method, it is possible to study of the hypersurface theory in $E^4$ which is analog the surface theory in $E^3$. Furthermore, the Gaussian curvature, mean curvature, fundamental forms and Dupin indicatrix of $M^3$ is introduced.
Keywords
Hypersurface
Gaussian curvature
Mean curvature
Euclidean geometry
Euclidean space
Mathematics
Curvature
Space (punctuation)
Surface (topology)
Mathematical analysis
Gaussian
Matrix (chemical analysis)
Pure mathematics
Geometry
Physics
Computer science
Subject Areas
Geometric Analysis and Curvature Flows
·Applied Mathematics ·Physical Sciences
Mathematics and Applications
·Geometry and Topology ·Physical Sciences
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