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Some type of semisymmetry on two classes of almost Kenmotsu manifolds

Dibakar Dey, Pradip Majhi (2021)

Communications in Mathematics

The object of the present paper is to study some types of semisymmetry conditions on two classes of almost Kenmotsu manifolds. It is shown that a ( k , μ ) -almost Kenmotsu manifold satisfying the curvature condition Q · R = 0 is locally isometric to the hyperbolic space 2 n + 1 ( - 1 ) . Also in ( k , μ ) -almost Kenmotsu manifolds the following conditions: (1) local symmetry ( R = 0 ) , (2) semisymmetry ( R · R = 0 ) , (3) Q ( S , R ) = 0 , (4) R · R = Q ( S , R ) , (5) locally isometric to the hyperbolic space 2 n + 1 ( - 1 ) are equivalent. Further, it is proved that a ( k , μ ) ' -almost Kenmotsu manifold satisfying...

Space-like Weingarten surfaces in the three-dimensional Minkowski space and their natural partial differential equations

Georgi Ganchev, Vesselka Mihova (2013)

Open Mathematics

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 surfaces...

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