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On Deszcz symmetries of Wintgen ideal submanifolds

Miroslava Petrović-Torgašev, Leopold C. A. Verstraelen (2008)

Archivum Mathematicum

It was conjectured in [26] that, for all submanifolds M n of all real space forms M ˜ n + m ( c ) , the Wintgen inequality ρ H 2 - ρ + c is valid at all points of M , whereby ρ is the normalised scalar curvature of the Riemannian manifold M and H 2 , respectively ρ , are the squared mean curvature and the normalised scalar normal curvature of the submanifold M in the ambient space M ˜ , and this conjecture was shown there to be true whenever codimension m = 2 . For a given Riemannian manifold M , this inequality can be interpreted as follows:...

On double-ruled hypersurfaces in 𝐑 4

Oldřich Kowalski, Zdeněk Vlášek (1997)

Commentationes Mathematicae Universitatis Carolinae

We classify locally the induced Riemannian metrics of all irreducible double-ruled hypersurfaces in 𝐑 4 .

On geometry of curves of flags of constant type

Boris Doubrov, Igor Zelenko (2012)

Open Mathematics

We develop an algebraic version of Cartan’s method of equivalence or an analog of Tanaka prolongation for the (extrinsic) geometry of curves of flags of a vector space W with respect to the action of a subgroup G of GL(W). Under some natural assumptions on the subgroup G and on the flags, one can pass from the filtered objects to the corresponding graded objects and describe the construction of canonical bundles of moving frames for these curves in the language of pure linear algebra. The scope...

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