On certain infinitesimal isometries of surfaces
Alois Švec (1988)
Czechoslovak Mathematical Journal
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Displaying similar documents to “On surfaces in with constant Gauss curvature”
On certain infinitesimal isometries of surfaces
Remark on surfaces in satisfying certain relations between covariant derivatives of the mean and Gauss curvatures
Karel Svoboda (1978)
Commentationes Mathematicae Universitatis Carolinae
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Space-like Weingarten surfaces in the three-dimensional Minkowski space and their natural partial differential equations
Georgi Ganchev, Vesselka Mihova (2013)
Open Mathematics
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On any space-like Weingarten surface in the three-dimensional Minkowski space we introduce locally natural principal parameters and prove that such a surface is determined uniquely up to motion by a special invariant function, which satisfies a natural non-linear partial differential equation. This result can be interpreted as a solution to the Lund-Regge reduction problem for space-like Weingarten surfaces in Minkowski space. We apply this theory to linear fractional space-like Weingarten...
Invariants and Bonnet-type theorem for surfaces in ℝ4
Georgi Ganchev, Velichka Milousheva (2010)
Open Mathematics
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In the tangent plane at any point of a surface in the four-dimensional Euclidean space we consider an invariant linear map ofWeingarten-type and find a geometrically determined moving frame field. Writing derivative formulas of Frenet-type for this frame field, we obtain eight invariant functions. We prove a fundamental theorem of Bonnet-type, stating that these eight invariants under some natural conditions determine the surface up to a motion. We show that the basic geometric classes...