Results 51 to 60 of about 730,375 (178)

Real hypersurfaces of type A in quarternionic projective space

International Journal of Mathematics and Mathematical Sciences, 1997
In this paper, under certain conditions on the orthogonal distribution 𝒟, we give a characterization of real hypersurfaces of type A in quaternionic projective space QPm.
U-Hang Ki, Young Jin Suh, Juan De Dios Pérez   +2 more
doaj   +1 more source

Involutions fixing HP1(2m)∪HP2(2m)∪HP(2n+1) of the fixed point set

Journal of Hebei University of Science and Technology, 2015
Let (Mr,T) be a smooth closed manifold of dimension r with a smooth involution T whose fixed point set is F=HP1(2m)∪HP2(2m)∪HP(2n+1)(m≥1), where HP(n) denotes the n-dimensional quaternionic projective space.
Suqian ZHAO
doaj   +1 more source

On real hypersurfaces in quaternionic projective space with 𝒟⊥-recurrent second fundamental tensor

International Journal of Mathematics and Mathematical Sciences, 1999
In this paper, we give a complete classification of real hypersurfaces in a quaternionic projective space QPm with 𝒟⊥-recurrent second fundamental tensor under certain condition on the orthogonal distribution 𝒟.
Young Jin Suh, Juan De Dios Pérez
doaj   +1 more source

Quaternionic holomorphic geometry: Pluecker formula, Dirac eigenvalue estimates and energy estimates of harmonic 2-tori [PDF]

, 2000
The paper develops the fundamentals of quaternionic holomorphic curve theory. The holomorphic functions in this theory are conformal maps from a Riemann surface into the 4-sphere, i.e., the quaternionic projective line.
Ferus, D., Leschke, K., Pedit, F., Pinkall, U.   +3 more
core   +3 more sources

Twistorial maps between quaternionic manifolds [PDF]

, 2008
We introduce a natural notion of quaternionic map between almost quaternionic manifolds and we prove the following, for maps of rank at least one: 1) A map between quaternionic manifolds endowed with the integrable almost twistorial structures is twistorial if and only if it is quaternionic.
arxiv   +1 more source

Integrability of quaternion-Kähler symmetric spaces [PDF]

arXiv, 2020
We find a necessary condition for the existence of an action of a Lie group $G$ by quaternionic automorphisms on an integrable quaternionic manifold in terms of representations of $\mathfrak{g}$. We check this condition and prove that a Riemannian symmetric space of dimension $4n$ for $n\geq 2$ has an invariant integrable almost quaternionic structure ...
arxiv  

Spectral representations of normal operators via Intertwining Quaternionic Projection Valued Measures [PDF]

Reviews in Mathematical Physics, Vol. 29, No. 10 (2017) 1750034 (73 pages), 2016
The possibility of formulating quantum mechanics over quaternionic Hilbert spaces can be traced back to von Neumann's foundational works in the thirties. The absence of a suitable quaternionic version of spectrum prevented the full development of the theory.
arxiv   +1 more source

Relative cubulation of relative strict hyperbolization

Journal of the London Mathematical Society, Volume 111, Issue 4, April 2025.
Abstract We prove that many relatively hyperbolic groups obtained by relative strict hyperbolization admit a cocompact action on a CAT(0)$\operatorname{CAT}(0)$ cubical complex. Under suitable assumptions on the peripheral subgroups, these groups are residually finite and even virtually special.
Jean‐François Lafont, Lorenzo Ruffoni
wiley   +1 more source

Quadratic Killing tensors on symmetric spaces which are not generated by Killing vector fields

Comptes Rendus. Mathématique
Every Killing tensor field on the space of constant curvature and on the complex projective space can be decomposed into the sum of symmetric tensor products of Killing vector fields (equivalently, every polynomial in velocities integral of the geodesic ...
Matveev, Vladimir S., Nikolayevsky, Yuri
doaj   +1 more source

Curvature of quaternionic skew‐Hermitian manifolds and bundle constructions

Mathematische Nachrichten, Volume 298, Issue 1, Page 87-112, January 2025.
Abstract This paper is devoted to a description of the second‐order differential geometry of torsion‐free almost quaternionic skew‐Hermitian manifolds, that is, of quaternionic skew‐Hermitian manifolds (M,Q,ω)$(M, Q, \omega)$. We provide a curvature characterization of such integrable geometric structures, based on the holonomy theory of symplectic ...
Ioannis Chrysikos, Vicente Cortés, Jan Gregorovič   +2 more
wiley   +1 more source