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Univerzální přírodní tvary

Leopold C. A. Verstraelen — 2007

Pokroky matematiky, fyziky a astronomie

Characterizations of conformally flat hypersurfaces

Johan Deprez; Piet A. Verheyen; Leopold C. A. Verstraelen — 1985

Czechoslovak Mathematical Journal

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 ${\tilde{M}}^{n + m} (c)$ , the Wintgen inequality $ρ \leq H^{2} - ρ^{⊥} + c$ 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 $\tilde{M}$ , 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:...

A pointwise inequality in submanifold theory

P. J. De Smet; F. Dillen; Leopold C. A. Verstraelen; L. Vrancken — 1999

Archivum Mathematicum

We obtain a pointwise inequality valid for all submanifolds $M^{n}$ of all real space forms $N^{n + 2} (c)$ with $n \geq 2$ and with codimension two, relating its main scalar invariants, namely, its scalar curvature from the intrinsic geometry of $M^{n}$ , and its squared mean curvature and its scalar normal curvature from the extrinsic geometry of $M^{n}$ in $N^{m} (c)$ .

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