Live briefing
Everything about Hypercomplex manifold
Manifold equipped with a quaternionic structure
In differential geometry, a hypercomplex manifold is a manifold with the tangent bundle equipped with an action by the algebra of quaternions in such a way that the quaternions define integrable almost complex structures. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Hypercomplex manifoldA 5-minute orientation
- Skim a recent paper: Algebraic dimension and complex subvarieties of hypercomplex nilmanifoldsInfluential work since 2022
- Read the landmark paper: Abelian Hypercomplex 8-Dimensional NilmanifoldsCited 31 times
- Go sideways: Quaternionic manifoldA closely related topic
- Go sideways: Quaternion-Kähler manifoldA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Abelian Hypercomplex 8-Dimensional Nilmanifolds
The KS-transformation in hypercomplex form and the quantization of the negative-energy orbit manifold of the Kepler problem
Integrability of the twistor space for a hypercomplex manifold
Hypercomplex manifolds and hyperholomorphic bundles
Hypercomplex Almost Abelian Solvmanifolds
Hypercomplex structures on Stiefel manifolds
A hypercomplex stiefel manifold
A manifold Fueter-Sce phenomenon in one hypercomplex variable
🆕 Influential since 2022
📚 Books worth reading
Open Library didn't respond; try again in a moment.
🔗 Related topics
- Quaternionic manifold In differential geometry, a quaternionic manifold is a quaternionic analog of a complex manifold. The definition is more complicated and technical than…
- Quaternion-Kähler manifold In differential geometry, a quaternion-Kähler manifold (or quaternionic Kähler manifold) is a Riemannian 4n-manifold whose Riemannian holonomy group is…
- Hyperkähler manifold In differential geometry, a hyperkähler manifold is a Riemannian manifold (M,g) endowed with three integrable almost complex structures I,J,K that are…
- Hopf manifold In complex geometry, a Hopf manifold (Hopf 1948) is obtained as a quotient of the complex vector space (with zero deleted) ( C n ∖ 0 ) {\displaystyle ({\mathbb…
- Einstein manifold In differential geometry and mathematical physics, an Einstein manifold is a Riemannian or pseudo-Riemannian differentiable manifold whose Ricci tensor…
- Edmond Bonan Edmond Bonan (born 27 January 1937 in Haifa, Mandatory Palestine) is a French mathematician, known particularly for his work on special holonomy. Although…
- Nearly Kähler manifold In mathematics, a nearly Kähler manifold is an almost Hermitian manifold M {\displaystyle M} , with almost complex structure J {\displaystyle J} , such…
- Quaternionic projective space In mathematics, quaternionic projective space is an extension of the ideas of real projective space and complex projective space, to the case where coordinates…