Ryszard Deszcz, Marian Hotloś, Zerrin Sentürk (2001)
Colloquium Mathematicae
We investigate curvature properties of hypersurfaces of a semi-Riemannian space form satisfying R·C = LQ(S,C), which is a curvature condition of pseudosymmetry type. We prove that under some additional assumptions the ambient space of such hypersurfaces must be semi-Euclidean and that they are quasi-Einstein Ricci-semisymmetric manifolds.
Fortin Boisvert, Mélisande (2007)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
Urs Lang, Viktor Schroeder (1997)
Annales scientifiques de l'École Normale Supérieure
Wortman, Kevin (2006)
Algebraic & Geometric Topology
Urs Lang (1992)
Mathematische Zeitschrift
Yves Colin de Verdiere (1977)
Inventiones mathematicae
Ilkka Holopainen, Seppo Rickman (1992)
Mathematische Annalen
Papantoniou, Bassil J., Shahid, M.Hasan (2001)
International Journal of Mathematics and Mathematical Sciences
Mitsuhiro Itoh (1986)
Mathematische Annalen
Hiroyuki Kamada, Shin Nayatani (2000/2001)
Séminaire de théorie spectrale et géométrie
Pedit, Franz, Pinkall, Ulrich (1998)
Documenta Mathematica
Dmitri Alekseevsky, Yoshinobu Kamishima (2004)
Open Mathematics
We define notion of a quaternionic and para-quaternionic CR structure on a (4n+3)-dimensional manifold M as a triple (ω1,ω2,ω3) of 1-forms such that the corresponding 2-forms satisfy some algebraic relations. We associate with such a structure an Einstein metric on M and establish relations between quaternionic CR structures, contact pseudo-metric 3-structures and pseudo-Sasakian 3-structures. Homogeneous examples of (para)-quaternionic CR manifolds are given and a reduction construction of non...
David Duchemin (2006)
Annales de l’institut Fourier
The conformal infinity of a quaternionic-Kähler metric on a -manifold with boundary is a codimension distribution on the boundary called quaternionic contact. In dimensions greater than , a quaternionic contact structure is always the conformal infinity of a quaternionic-Kähler metric. On the contrary, in dimension , we prove a criterion for quaternionic contact structures to be the conformal infinity of a quaternionic-Kähler metric. This allows us to find the quaternionic-contact structures...
Andrew Swann, Piotr Z. Kobak (1993)
Mathematische Annalen
Tamás Hausel (2005)
Open Mathematics
Building on a recent paper [8], here we argue that the combinatorics of matroids are intimately related to the geometry and topology of toric hyperkähler varieties. We show that just like toric varieties occupy a central role in Stanley’s proof for the necessity of McMullen’s conjecture (or g-inequalities) about the classification of face vectors of simplicial polytopes, the topology of toric hyperkähler varieties leads to new restrictions on face vectors of matroid complexes. Namely in this paper...
Simon Salamon (1982)
Inventiones mathematicae
Andrew John Sommese (1974)
Mathematische Annalen
Jingyi Chen, Jiayu Li (2005)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
Let and be hyperkähler manifolds. We study stationary quaternionic maps between and . We first show that if there are no holomorphic 2-spheres in the target then any sequence of stationary quaternionic maps with bounded energy subconverges to a stationary quaternionic map strongly in . We then find that certain tangent maps of quaternionic maps give rise to an interesting minimal 2-sphere. At last we construct a stationary quaternionic map with a codimension-3 singular set by using the embedded...
K. Galicki, H.B. Jr. Lawson (1988)
Mathematische Annalen
Włodzimierz Jelonek (2000)
Annales Polonici Mathematici
The aim of this paper is to give an easy explicit description of 3-K-contact structures on certain SO(3)-principal fibre bundles over quaternionic-Kähler manifolds.