In mathematics, quaternionic projective space is an extension of the ideas of real projective space and complex projective space, to the case where coordinates...

inequality for complex projective space Projective Hilbert space Quaternionic projective space Real projective space Complex affine space K3 surface Besse,...

w_{1}} , which has degree 1. Complex projective space Quaternionic projective space Lens space Real projective plane See the table of Don Davis for a...

dearth of examples, and exclude spaces like quaternionic projective space which should clearly be considered as quaternionic manifolds. Marcel Berger's 1955...

point", which is subject to the axioms of projective geometry. For some such set of axioms, the projective spaces that are defined have been shown to be...

connected symmetric spaces. (For example, the universal cover of a real projective plane is a sphere.) Second, the product of symmetric spaces is symmetric,...

conventional projective space to a point. More concretely, in a real projective space, complex projective space or quaternionic projective space K P n {\displaystyle...

subcategories. Euclidean space, Rn n-sphere, Sn n-torus, Tn Real projective space, RPn Complex projective space, CPn Quaternionic projective space, HPn Flag manifold...

"Physical space as a quaternion structure, I: Maxwell equations. A brief Note". arXiv:math-ph/0307038. Kravchenko, Vladislav (2003). Applied Quaternionic Analysis...

and real projective spaces with their standard metrics, along with hyperbolic space. The complex projective space, quaternionic projective space, and Cayley...

coordinate space Cn+1 fibers naturally over the complex projective space CPn with circles as fibers, and there are also real, quaternionic, and octonionic...

the complex projective plane, and finite, such as the Fano plane. A projective plane is a 2-dimensional projective space. Not all projective planes can...

the corresponding Wolf space is the quaternionic projective space H P n {\displaystyle \mathbb {HP} _{n}} of (right) quaternionic lines through the origin...

explains how one can associate a unique Wolf space to each of the simple complex Lie groups. Quaternionic discrete series representation Besse, Arthur...

Complex projective space CPn is a 2n-dimensional manifold. Quaternionic projective space HPn is a 4n-dimensional manifold. Manifolds related to projective space...

is a principal S p ( 1 ) {\displaystyle Sp(1)} -bundle over quaternionic projective space H P n {\displaystyle \mathbb {H} \mathbb {P} ^{n}} . We then...

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

group, Sp(2n, R), on the phase space. Hamiltonian mechanics Metaplectic group Orthogonal group Paramodular group Projective unitary group Representations...

tautological line bundle on projective space. The projectivization P ( V ) {\displaystyle \mathbf {P} (V)} of a vector space V {\displaystyle V} over a...

7-sphere, which can be acquired by embedding the 7-sphere in a quaternionic projective space, with this giving a gauge group of SO ( 5 ) × SU ( 2 ) {\displaystyle...

Riemannian symmetric spaces. Basic examples of Riemannian symmetric spaces are Euclidean space, spheres, projective spaces, and hyperbolic spaces, each with their...

to the algebraic concept of projective modules and gives rise to a common intuition throughout mathematics: "projective modules over commutative rings...

symmetric spaces of noncompact type, together with real and quaternionic hyperbolic spaces, classification to which must be added one exceptional space, the...

England Higgs prime, H p n {\displaystyle Hp_{n}} HPN (gene) Quaternionic projective space, H P n {\displaystyle \mathbb {H} \mathrm {P} ^{n}} Westchester...

skew-Hermitian sesquilinear forms defined on real, complex and quaternionic finite-dimensional vector spaces. Of these, the complex classical Lie groups are four...

"The Grassmann method in projective geometry" A compilation of three notes on the application of exterior algebra to projective geometry C. Burali-Forti...

space of spinors, in a way that genuinely depends on the homotopy class. In mathematical terms, spinors are described by a double-valued projective representation...

respect to the Riemannian metric g {\displaystyle g} and satisfy the quaternionic relations I 2 = J 2 = K 2 = I J K = − 1 {\displaystyle I^{2}=J^{2}=K^{2}=IJK=-1}...

its normal spaces maps the manifold onto itself. Analogous Veronese embeddings are constructed for complex and quaternionic projective spaces, as well as...

equality is attained by the symmetric metric of the projective plane. Meanwhile, in the quaternionic case, the symmetric metric on H P 2 {\displaystyle...