Results 111 to 120 of about 145 (132)
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Weakly symmetric spaces in complex and quaternionic space forms
Archiv Der Mathematik, 1995We prove that some classes of generic submanifolds which include homogeneous real hypersurfaces in complex and quaternionic space forms are weakly symmetric spaces. In our method, the reflection with respect to a submanifold plays a central role.
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D-einstein real hypersurfaces of quaternionic space forms
Annali Di Matematica Pura Ed Applicata, 2000It is known that the only Einstein real hypersurface in a quaternionic projective space \(QP^m\), \(m \geq 2\), is a geodesic hypersphere of a certain radius. Moreover, there are no Einstein real hypersurfaces in quaternionic hyperbolic space \(QH^m\), \(m \geq 2\).
Juan de Dios Perez, Miguel Ortega
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Real Hypersurfaces in Quaternionic Space Forms Satyisfying Axioms of Planes
Acta Mathematica Hungarica, 2001zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Miguel Ortega
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Inequalities for the Casorati curvatures of slant submanifolds in quaternionic space forms [PDF]
Journal of Inequalities and Applications, 2014 Abstract In this paper we prove two sharp inequalities that relate the normalized scalar curvature with the Casorati curvature for a slant submanifold in a quaternionic space form. Moreover, we show that in both cases, the equality at all points characterizes the invariantly quasi-umbilical submanifolds.
Gabriel-Eduard Vilcu +2 more
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Basic inequalities for submanifolds of quaternionic space forms with a quarter-symmetric connection
Journal of Geometry and Physics, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mehraj Ahmad Lone
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On a class of QR-submanifolds of quaternion space forms
Publicationes Mathematicae Debrecen, 1999The author studies \(QR\)-submanifolds \(M\) of a quaternion space form \(N(c)\) such that every geodesic of \(M\) is a circle of \(N(c)\) and proves that either \(c=0\) or \(M\) is a totally real submanifold.
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Ricci curvature of quaternion slant submanifolds in quaternion space forms
2012Summary: In this article, we obtain sharp estimates for the Ricci curvature of quaternion slant, bi-slant and semi-slant submanifolds in a quaternion space form, in terms of the squared mean curvature.
Shukla, S. S., Rao, Pawan Kumar
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Naturally reductive homogeneous real hypersurfaces in quaternionic space forms
Journal of the Australian Mathematical Society, 2003AbstractWe determine the naturally reductive homogeneous real hypersurfaces in the family of curvature-adapted real hypersurfaces in quaternionic projective space HPn(n ≥ 3). We conclude that the naturally reductive curvature-adapted real hypersurfaces in HPn are Q-quasiumbilical and vice-versa.
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Quaternionic Kähler structures on the tangent bundle of a complex space form
1999The authors construct a family of quaternionic Kähler structures on the tangent bundle of any complex space form of complex dimension at least 3. The quaternionic Kähler structure depends on the choice of a positive function on the half-line, satisfying some bounds.
MARCHIAFAVA, Stefano +2 more
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