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The Clairaut's theorem on rotational surfaces in pseudo-Euclidean 4-space with index 2

Fatma Almaz, Mihriban A. Külahci (2024)

Commentationes Mathematicae Universitatis Carolinae

Clairaut’s theorem is expressed on the surfaces of rotation in semi Euclidean 4-space. Moreover, the general equations of time-like geodesic curves are characterized according to the results of Clairaut's theorem on the hyperbolic surfaces of rotation and the elliptic surface of rotation, respectively.

The Dolbeault operator on Hermitian spin surfaces

Bodgan Alexandrov, Gueo Grantcharov, Stefan Ivanov (2001)

Annales de l’institut Fourier

We prove the vanishing of the kernel of the Dolbeault operator of the square root of the canonical line bundle of a compact Hermitian spin surface with positive scalar curvature. We give lower estimates of the eigenvalues of this operator when the conformal scalar curvature is non -negative.

The gap phenomenon in the dimension study of finite type systems

Boris Kruglikov (2012)

Open Mathematics

Several examples of gaps (lacunes) between dimensions of maximal and submaximal symmetric models are considered, which include investigation of number of independent linear and quadratic integrals of metrics and counting the symmetries of geometric structures and differential equations. A general result clarifying this effect in the case when the structure is associated to a vector distribution, is proposed.

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