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Constant curvature ( 2 + 1 ) -spacetimes and projective structures

Francesco Bonsante (2004/2005)

Séminaire de théorie spectrale et géométrie

Nous illustrons une classification des espace-temps (2+1) globalement hyperboliques a courboure constant, en terms de certaines structures projectives complexes portées par les surfaces de niveau de leur temps cosmologique canonique. Ceci derive d’une theorie des rotations de Wick canoniques, developpée en collaboration avec Riccardo Benedetti [6], qui sera egalement brievement illustrée.

Constant Jacobi osculating rank of 𝐔 ( 3 ) / ( 𝐔 ( 1 ) × 𝐔 ( 1 ) × 𝐔 ( 1 ) )

Teresa Arias-Marco (2009)

Archivum Mathematicum

In this paper we obtain an interesting relation between the covariant derivatives of the Jacobi operator valid for all geodesic on the flag manifold M 6 = U ( 3 ) / ( U ( 1 ) × U ( 1 ) × U ( 1 ) ) . As a consequence, an explicit expression of the Jacobi operator independent of the geodesic can be obtained on such a manifold. Moreover, we show the way to calculate the Jacobi vector fields on this manifold by a new formula valid on every g.o. space.

Constant scalar curvature hypersurfaces with spherical boundary in Euclidean space.

Luis J. Alías, J. Miguel Malacarne (2002)

Revista Matemática Iberoamericana

It is still an open question whether a compact embedded hypersurface in the Euclidean space with constant mean curvature and spherical boundary is necessarily a hyperplanar ba1l or a spherical cap, even in the simplest case of a compact constant mean curvature surface in R3 bounded by a circle. In this paper we prove that this is true for the case of the scalar curvature. Specifica1ly we prove that the only compact embedded hypersurfaces in the Euclidean space with constant scalar curvature and...

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