Quaternionic Projective Space Research Articles

Lagrangians of N = 2 supergravity-matter systems

We present explicit expressions for general actions of vector and scalar multiplets coupled to N = 2 supergravity. We outline their construction which is based on the superconformal tensor calculus. The vector multiplets may be associated with a gauge group G which may also act on the scalar multiplets. The latter are naturally described in terms of quaternions; in the simplest case their kinetic terms define a nonlinear sigma model of a quaternionic projective space. We give an extension of the vector multiplet action which is not obtained from a chiral superspace density, and contains a Chern-Simons-type term. Transformation rules are given and the conditions for supersymmetry breaking are defined.

Actions of symplectic groups on a product of quaternion projective spaces

Actions of symplectic groups on a product of quaternion projective spaces

Stable Self Maps of the Quaternionic (Quasi-) Projective Space

Let HP (resp. CP) be the quaternionic (resp. complex) ^-dimensional projective space. QP denotes the quaternionic quasi-projective space of dimension 4n—l. For a pointed space X we denote the «-th reduced suspension by 2X and denote the associated suspension spectrum by S°°X. We denote the group of stable homotopy classes of stable maps from 2°°X to 2~Y by [X, Y]. n*(X) denotes the stable homotopy group of X. Throughout this paper we shall denote the homotopy class of a map / by the same letter /for abbreviation.

On the Stable Hurewicz Image of Some Stunted Projective Spaces, I

In the previous paper [3], we investigated the order of the cokernel of the stable Hurewicz homomorphism on the stunted projective space HPTM. In this paper, we consider the analogous problem for the quaternionic quasi-projective spaces. Let QP (l^n^oo) be the (4n— l)-dimensional quaternionic quasi-projective space, and QP^=QP/QP~ (2^k^ri) (denoted by Qn.n-k+1 in James [4]) be the stunted quasi-projective space. For the complex projective space CP and the quaternionic projective space HP, it is known (cf. James [5]) that QP°° is a cofiber of the projection q : CP^-^HP. Thus there is a cofiber sequence

The Construction of a Class of Harmonic Maps to Quaternionic Projective Space

The Construction of a Class of Harmonic Maps to Quaternionic Projective Space

ON THE EXTRINSIC GEOMETRIC PROPERTIES OF PARABOLIC SURFACES AND TOPOLOGICAL PROPERTIES OF SADDLE SURFACES IN SYMMETRIC SPACES OF RANK ONE

This paper investigates the metric structure of compact -parabolic surfaces and topological properties of -saddle surfaces in the sense of Sefel' in symmetric spaces of rank one, namely, spherical space , complex projective space , and quaternion projective space . It turns out that -parabolic surfaces for large are totally geodesic spheres in , totally geodesic complex projective spaces in , and totally geodesic quaternion projective spaces in . It follows that surfaces of nonpositive extrinsic -dimensional curvature, under a natural restriction on the codimension of the embedding, are totally geodesic surfaces in , and . Saddle surfaces for small have restrictions on the homology and cohomology groups. Since surfaces of nonpositive -dimensional extrinsic curvature for small codimension of the embedding are -saddle surfaces, they also have degeneracies in the homology and cohomology groups.Bibliography: 27 titles.

On the non-existence of smooth actions of complex sympletic group on cohomology quaternion projective spaces

On the non-existence of smooth actions of complex sympletic group on cohomology quaternion projective spaces

Quaternion CR-submanifolds of quaternion manifolds

A quaternion manifold (or quaternion Kaehlerian manifold [10]) is defined as a Riemannian manifold whose holonomy group is a subgroup of Sp(l). Sp(m)=Sp(l)xSp(m)/{±1}. The quaternion projective space QP, its noncompact dual and the quaternion number space Q are three important examples of quaternion manifolds. It is well-known that on a quaternion manifold M, there exists a 3-dimensional vector bundle E of tensors of type (1, 1) with local cross-section of almost Hermitian structures satisfying certain conditions (see § 2 for details). A submanifold N in a quaternion manifold M is called a quaternion (respectively, totally real) submanifold if each tangent space of N is carried into itself (respectively, the normal space) by each section in E. It is known that every quaternion submanifold in any quaternion manifold is always totally geodesic. So it is more interesting to study a more general class of submanifolds than quaternion submanifolds. The main purpose of this paper is to establish the general theory of quaternion Ci?-submanifolds in a quaternion manifold which generalizes the theory of quaternion submanifolds and the theory of totally real submanifolds. It is proved in section 3 that such submanifolds are characterized by a simple equation in terms of the curvature tensor of a quaternion-space-form. In section 4 we shall study the integrability of the two natural distributions on a quaternion Ci?-submanifold. In section 5 we obtain some basic lemmas for quaternion Ci?-submamfolds. In particular, we shall obtain two fundamental lemmas which play important role in this theory. Several applications of the fundamental lemmas are given in section 6. In section 7 we study quaternion C7?-submanifolds which are foliated by totally geodesic, totally real submanifolds. In the last section we give an example of a quaternion Ci?-submanifold of an almost quaternion metric manifold on which the totally real distribution is not integrable.

Some totally real submanifolds in a quaternion projective space

Some totally real submanifolds in a quaternion projective space

Totally real submanifolds of a quaternion projective space

Totally real submanifolds of a quaternion projective space

Four-dimensional σ-model on quaternionic projective space

A four-dimensional σ-model based on the quaternionic projective space is constructed. The model possesses SU(2) gauge invariance and has one-instanton solutions analogous to those in the CP n model in D=2.

On stable James numbers of stunted complex or quaternionic projective spaces

On stable James numbers of stunted complex or quaternionic projective spaces

Jacobi fields and geodesic spheres

SynopsisThis is a contribution to the general problem of determining the extent to which the geometry of a riemannian manifold is determined by properties of its geodesic spheres. In particular we show that total umbilicity of geodesic spheres determines riemannian manifolds of constant sectional curvature; quasi-umbilicity of geodesic spheres determines Kähler and nearly-Kähler manifolds of constant holomorphic sectional curvature; and the condition that geodesic spheres have only two different principal curvatures, one having multiplicity 3, determines manifolds locally isometric to the quaternionic projective spaces. The use of Jacobi vector fields leads to a unified treatment of these different cases.

Classification of compact transformation groups on cohomology quaternion projective spaces with codimension one orbits

Classification of compact transformation groups on cohomology quaternion projective spaces with codimension one orbits

Group Actions on Homology Quaternionic Projective Planes

A class of ${{\mathbf {Z}}_p}$-actions, resembling well-known actions on the quaternionic projective plane, is defined and studied. The existence of such actions on a closed homology quaternionic projective plane is shown to imply numerical restrictions on the manifold’s Pontrjagin classes. One consequence is that for $p = 3$, or 5, infinitely many smooth manifolds of this type admit no smooth ${{\mathbf {Z}}_p}$-actions.

Real submanifolds in a quaternionic projective space

Real submanifolds in a quaternionic projective space

Group actions on homology quaternionic projective planes

A class of Z p {{\mathbf {Z}}_p} -actions, resembling well-known actions on the quaternionic projective plane, is defined and studied. The existence of such actions on a closed homology quaternionic projective plane is shown to imply numerical restrictions on the manifold’s Pontrjagin classes. One consequence is that for p = 3 p = 3 , or 5, infinitely many smooth manifolds of this type admit no smooth Z p {{\mathbf {Z}}_p} -actions.

Smooth ${\rm Sp}(n)$-actions on cohomology quaternion projective spaces

Smooth ${\rm Sp}(n)$-actions on cohomology quaternion projective spaces

On a characterization of quaternion projective space by differential equations

On a characterization of quaternion projective space by differential equations

Structural theorems for topological actions of Z2-torion real, complex and quaternionic projective spaces

Structural theorems for topological actions of Z2-torion real, complex and quaternionic projective spaces