QR-Dimension in a Quaternionic Projective Space QP under Some Curvature Conditions
نویسندگان
چکیده
at each point x in M, then M is called a QR-submanifold of r QR-dimension, where ] denotes the complementary orthogonal distribution to ] in TM (cf. [1–3]). Real hypersurfaces, which are typical examples of QR-submanifold with r = 0, have been investigated by many authors (cf. [2–9]) in connection with the shape operator and the induced almost contact 3-structure (for definition, see [10–13]). In their paper [2, 3], Kwon and Pak had studied QR-submanifolds of (p − 1) QR-dimension isometrically immersed in a quaternionic projective space QP and proved the following theorem as a quaternionic analogy to theorems given in [14, 15], which are natural extensions of theorems proved in [6] to the case of QR-submanifolds with (p − 1) QR-dimension and also extensions of theorems in [16].
منابع مشابه
Certain QR-submanifolds of maximal QR-dimension in a quaternionic space form
The purpose of this paper is to study n-dimensional QRsubmanifolds of maximal QR-dimension isometrically immersed in a quaternionic space form and to classify such submanifolds under certain conditions concerning the second fundamental form and the induced almost contact 3-structure. M.S.C. 2010: 53C40, 53C25.
متن کاملCertain Conditions on the Ricci Tensor of Real Hypersurfaces in Quaternionic Projective Spaces
The purpose of this paper is to classify real hypersurfaces of quaternionic projective spaces whose Ricci tensor satisfy a pair of conditions on the maximal quaternionic distribution D? = Span fU1; U2; U3g. x0. Introduction Throughout this paper let us denote by M a connected real hypersurface in a quaternionic projective space QP, m=3, endowed with the metric g of constant quaternionic section...
متن کاملA characterization of quaternionic projective space by the conformal-Killing equation
We prove that a compact quaternionic-Kähler manifold of dimension 4n ≥ 8 admitting a conformal-Killing 2-form which is not Killing, is isomorphic to the quaternionic projective space, with its standard quaternionicKähler structure.
متن کاملResponse to the Comment by G. Emch on Projective Group Representations in Quaternionic Hilbert Space
We discuss the differing definitions of complex and quaternionic projective group representations employed by us and by Emch. The definition of Emch (termed here a strong projective representation) is too restrictive to accommodate quaternionic Hilbert space embeddings of complex projective representations. Our definition (termed here a weak projective representation) encompasses such embedding...
متن کاملOn Real Hypersurfaces in Quaternionic Projective Space with D⊥-recurrent Second Fundamental Tensor
In this paper, we give a complete classification of real hypersurfaces in a quaternionic projective space QPm with ⊥-recurrent second fundamental tensor under certain condition on the orthogonal distribution .
متن کامل