In differential geometry, a quaternionic manifold is a quaternionic analog of a complex manifold. The definition is more complicated and technical than...

the quaternionic relations I 2 = J 2 = K 2 = I J K = − 1 {\displaystyle I^{2}=J^{2}=K^{2}=IJK=-1} . In particular, it is a hypercomplex manifold. All...

manifold or equivalently one whose first Chern class vanishes. Complex dimension Complex analytic variety Quaternionic manifold Real-complex manifold...

differential geometry, a quaternion-Kähler manifold (or quaternionic Kähler manifold) is a Riemannian 4n-manifold whose Riemannian holonomy group is a subgroup...

Quaternionic manifold – Concept in geometry Quaternionic matrix – Concept in linear algebra Quaternionic polytope – Concept in geometry Quaternionic projective...

vanishing pure spinor then M is a generalized Calabi–Yau manifold. Almost quaternionic manifold – Concept in geometryPages displaying short descriptions...

Stiefel manifold V k ( C n ) {\displaystyle V_{k}(\mathbb {C} ^{n})} of orthonormal k-frames in C n {\displaystyle \mathbb {C} ^{n}} and the quaternionic Stiefel...

In mathematics, quaternionic analysis is the study of functions with quaternions as the domain and/or range. Such functions can be called functions of...

\mathbb {H} .} Quaternionic projective space of dimension n is usually denoted by H P n {\displaystyle \mathbb {HP} ^{n}} and is a closed manifold of (real)...

RPn Complex projective space, CPn Quaternionic projective space, HPn Flag manifold Grassmann manifold Stiefel manifold Lie groups provide several interesting...

hyperbolic space, quaternionic hyperbolic space, and Cayley hyperbolic space, which are instead analogues of hyperbolic space. Grassmannian manifolds also carry...

compact manifolds. Real projective space RPn is a n-dimensional manifold. Complex projective space CPn is a 2n-dimensional manifold. Quaternionic projective...

not assumed to be integrable, the manifold is called quaternionic, or almost hypercomplex. Every hyperkähler manifold is also hypercomplex. The converse...

mathematics, particularly in differential geometry, an Osserman manifold is a Riemannian manifold in which the characteristic polynomial of the Jacobi operator...

Even-dimensional Hopf manifolds admit hypercomplex structure. The Hopf surface is the only compact hypercomplex manifold of quaternionic dimension 1 which...

incompatibility (help) Kraines, Vivian Yoh (1965), "Topology of quaternionic manifolds", Bull. Amer. Math. Soc., 71, 3, 1 (3): 526–7, doi:10.1090/s0002-9904-1965-11316-7...

the simple complex Lie groups. Quaternionic discrete series representation Besse, Arthur L. (2008), Einstein Manifolds, Classics in Mathematics, Berlin:...

In differential geometry, a G-structure on an n-manifold M, for a given structure group G, is a principal G-subbundle of the tangent frame bundle FM (or...

The Lie algebra of Sp(n) is given by the quaternionic skew-Hermitian matrices, the set of n-by-n quaternionic matrices that satisfy A + A † = 0 {\displaystyle...

theories, (real) KO-theory and (quaternionic) KSp-theory, associated to the real orthogonal group and the quaternionic symplectic group, respectively....

the quaternionic relations I 2 = J 2 = K 2 = I J K = − Id {\displaystyle I^{2}=J^{2}=K^{2}=IJK=-\operatorname {Id} } . Thus, hyper-Kähler manifolds are...

(or quaternionic spin structure) is a special classifying map that can exist for orientable manifolds. Such manifolds are called spinh manifolds. H stands...

N=2 Supergravity that in this case, the Higgs branch must be a quaternionic Kähler manifold. In extended supergravities with N>2 the moduli space must always...

giving the signature see Hirzebruch signature theorem. There is also a quaternionic Pontryagin class, for vector bundles with quaternion structure. Chern–Simons...

of cardinal directions. This means that a 3-sphere is an example of a 3-manifold. In coordinates, a 3-sphere with center (C0, C1, C2, C3) and radius r is...

{\displaystyle \mathbb {CP} ^{2}} ( n = 4 {\displaystyle n=4} ), of the quaternionic projective plane H P 2 {\displaystyle \mathbb {HP} ^{2}} ( n = 8 {\displaystyle...

multiple of the metric. Hyperbolic space Quaternionic hyperbolic space Arthur Besse (1987), Einstein manifolds, Springer, p. 180. Cano, Angel; Navarrete...

projective space CPn with circles as fibers, and there are also real, quaternionic, and octonionic versions of these fibrations. In particular, the Hopf...

ISBN 978-0-12-329650-4. Kraines, Vivian Yoh (1965), "Topology of quaternionic manifolds", Bull. Amer. Math. Soc., 71, 3, 1 (3): 526–527, doi:10...

doi:10.1007/978-1-4612-0979-9. ISBN 978-1-4612-0979-9. Besse, Einstein manifolds ISBN 0-387-15279-2 Helgason, Differential geometry, Lie groups, and symmetric...