Results 71 to 80 of about 784 (176)

Real hypersurfaces in Kähler manifolds [PDF]

Asian Journal of Mathematics, 2001
This paper is concerned with the geometry of embedded real hypersurfaces in a Kähler manifold, where isomorphisms are both holomorphic and isometric in the underlying Riemannian structure. The author introduces their local invariants and compatibility relations, solves the local realization problem, and gives a characterization of the metric sphere in \
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On the Work of Cartan and Münzner on Isoparametric Hypersurfaces

Axioms
A hypersurface Mn in a real space form Rn+1, Sn+1, or Hn+1 is isoparametric if it has constant principal curvatures. This paper is a survey of the fundamental work of Cartan and Münzner on the theory of isoparametric hypersurfaces in real space forms, in
Thomas E. Cecil, Patrick J. Ryan
doaj   +1 more source

On holomorphic one-forms transverse to closed hypersurfaces

Anais da Academia Brasileira de Ciências, 2003
In this note we announce some achievements in the study of holomorphic distributions admitting transverse closed real hypersurfaces. We consider a domain with smooth boundary in the complex affine space of dimension two or greater. Assume that the domain
Toshikazu Ito, Bruno Scárdua
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Singularity of non‐pluripolar cohomology classes

Bulletin of the London Mathematical Society, Volume 58, Issue 9, September 2026.
Abstract We establish a relation between Lelong numbers and the full mass property of relative non‐pluripolar products. We use this relation to prove that if the restricted volume of a big class α$\alpha$ along an effective divisor D$D$ has full mass, then the Lelong numbers of the non‐pluripolar class ⟨αn−1⟩$\langle \alpha ^{n-1}\rangle$ at every ...
Duc‐Bao Nguyen, Shuang Su, Duc‐Viet Vu   +2 more
wiley   +1 more source

Defining equations for real analytic real hypersurfaces in 𝐶ⁿ [PDF]

Transactions of the American Mathematical Society, 1986
A defining function for a real analytic real hypersurface can be uniquely written as 2 Re ⁡
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Isoparametric and Dupin Hypersurfaces

Symmetry, Integrability and Geometry: Methods and Applications, 2008
A hypersurface $M^{n−1}$ in a real space-form $R^n$, $S^n$ or $H^n$ is isoparametric if it has constant principal curvatures. For $R^n$ and $H^n$, the classification of isoparametric hypersurfaces is complete and relatively simple, but as Élie Cartan ...
Thomas E. Cecil
doaj   +1 more source

Nonexistence of Homogeneous Levi-Flat Hypersurfaces in ${\mathbb{C}\mathbb{P}}^2$

Mathematics
We investigate the longstanding question of whether compact Levi-flat hypersurfaces exist in the complex projective plane CP2. While the nonexistence of closed real-analytic Levi-flat hypersurfaces in CPn for n>2 is well known, the case n=2 remains open.
Abdel Rahman Al-Abdallah
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REAL HYPERSURFACES IN COMPLEX MANIFOLDS [PDF]

Acta Mathematica, 1974
Chern, S. S., Moser, J. K.
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Real Hypersurfaces with Many Simple Singularities

Revista Matemática Complutense, 2005
This paper extends the results of \textit{E. Shustin} and \textit{E. Westenberger} [J. Lond. Math. Soc., II. Ser. 70, No. 3, 609--624 (2004; Zbl 1075.14034)] on the existence of algebraic hypersurfaces with prescribed simple singularities to the real case.
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What Is a Simple Liquid?

Physical Review X, 2012
This paper is an attempt to identify the real essence of simplicity of liquids in John Locke’s understanding of the term. Simple liquids are traditionally defined as many-body systems of classical particles interacting via radially symmetric pair ...
Trond S. Ingebrigtsen, Thomas B. Schrøder, Jeppe C. Dyre   +2 more
doaj   +1 more source