scholarly journals Totally Real Submanifolds in a Quaternion Space Form

2004 ◽  
Vol 54 (2) ◽  
pp. 341-346
Author(s):  
Mehmet Bektaş
Keyword(s):  
Space Form ◽  
Real Submanifolds ◽  
Quaternion Space ◽  
Totally Real

scholarly journals A class of C-totally real submanifolds of Sasakian space forms

1998 ◽  
Vol 65 (1) ◽  
pp. 120-128
Author(s):  
Filip Defever ◽  
Ion Mihai ◽  
Leopold Verstraelen
Keyword(s):  
Riemannian Manifold ◽  
Mean Curvature ◽  
Space Form ◽  
Sasakian Space Form ◽  
Real Submanifolds ◽  
Space Forms ◽  
Sasakian Space Forms ◽  
Totally Real ◽  
Real Complex

AbstractRecently, Chen defined an invariant δM of a Riemannian manifold M. Sharp inequalities for this Riemannian invariant were obtained for submanifolds in real, complex and Sasakian space forms, in terms of their mean curvature. In the present paper, we investigate certain C-totally real submanifolds of a Sasakian space form M2m+1(C)satisfying Chen's equality.

scholarly journals Totally real pseudo-umbilical submanifolds of a quaternion space form

1998 ◽  
Vol 40 (1) ◽  
pp. 109-115 ◽  
Author(s):  
Huafei Sun
Keyword(s):  
Riemannian Manifold ◽  
Projective Space ◽  
Sectional Curvature ◽  
Space Form ◽  
Real Plane ◽  
Quaternion Space ◽  
Real Submanifold ◽  
Totally Real Submanifold ◽  
Totally Real

Let M(c) denote a 4n-dimensional quaternion space form of quaternion sectional curvature c, and let P(H) denote the 4n-dimensional quaternion projective space of constant quaternion sectional curvature 4. Let N be an n-dimensional Riemannian manifold isometrically immersed in M(c). We call N a totally real submanifold of M(c) if each tangent 2-plane of N is mapped into a totally real plane in M (c). B. Y. Chen and C. S. Houh proved in [1].

Totally real submanifolds in a generalized complex space form

2016 ◽  
Vol 10 (02) ◽  
pp. 1750035
Author(s):  
Majid Ali Choudhary
Keyword(s):  
Fundamental Form ◽  
Complex Space ◽  
Space Form ◽  
Second Fundamental Form ◽  
Text Structure ◽  
Complex Space Form ◽  
Real Submanifolds ◽  
Constant Length ◽  
Generalized Complex ◽  
Totally Real

In the present paper, we investigate totally real submanifolds in generalized complex space form. We study the [Formula: see text]-structure in the normal bundle of a totally real submanifold and derive some integral formulas computing the Laplacian of the square of the second fundamental form and using these formulas, we prove a pinching theorem. In fact, the purpose of this note is to generalize results proved in B. Y. Chen and K. Ogiue, On totally real manifolds, Trans. Amer. Math. Soc. 193 (1974) 257–266, S. S. Chern, M. Do Carmo and S. Kobayashi, Minimal submanifolds of a sphere with second fundamental form of constant length, in Functional Analysis and Related Fields (Springer-Verlag, 1970), pp. 57–75 to the case, when the ambient manifold is generalized complex space form.

scholarly journals Totally real submanifolds of a complex space form

1996 ◽  
Vol 19 (1) ◽  
pp. 39-44 ◽  
Author(s):  
U-Hang Ki ◽  
Young Ho Kim
Keyword(s):  
Mean Curvature ◽  
Complex Space ◽  
Space Form ◽  
Curvature Vector ◽  
Complex Space Form ◽  
Mean Curvature Vector ◽  
Parallel Mean Curvature Vector ◽  
Real Submanifolds ◽  
Parallel Mean Curvature ◽  
Totally Real

Totally real submanifolds of a complex space form are studied. In particular, totally real submanifolds of a complex number space with parallel mean curvature vector are classified.

scholarly journals C-totally real submanifolds in (κ,μ)-contact space forms

2003 ◽  
Vol 67 (1) ◽  
pp. 51-65 ◽  
Author(s):  
Mukut Mani Tripathi ◽  
Jeong-Sik Kim
Keyword(s):  
Ricci Curvature ◽  
Mean Curvature ◽  
Space Form ◽  
Real Submanifolds ◽  
Space Forms ◽  
Left Hand ◽  
Real Submanifold ◽  
The Right ◽  
Totally Real ◽  
Contact Space

We obtain a basic B,-Y. Chen's inequality for a C-totally real submanifold in a (κ,μ)-contact space form involving intrinsic invariants, namely the scalar curvature and the sectional curvatures of the submanifold on left hand side and the main extrinsic invariant, namely the squared mean curvature on the right hand side. Inequalities between the squared mean curvature and Ricci curvature and between the squared mean curvature and κ-Ricci curvature are also obtained. These results are applied to get corresponding results for C-totally real submanifolds in a Sasakian space form.

scholarly journals Submanifolds in Normal Complex Contact Manifolds

Mathematics ◽  
2019 ◽  
Vol 7 (12) ◽  
pp. 1195
Author(s):  
Adela Mihai ◽  
Ion Mihai
Keyword(s):  
Present Article ◽  
Space Form ◽  
Real Submanifolds ◽  
Maximum Dimension ◽  
Contact Manifolds ◽  
Basic Properties ◽  
Normal Complex ◽  
Contact Metric Manifolds ◽  
Totally Real ◽  
Chen Inequality

In the present article we initiate the study of submanifolds in normal complex contact metric manifolds. We define invariant and anti-invariant ( C C -totally real) submanifolds in such manifolds and start the study of their basic properties. Also, we establish the Chen first inequality and Chen inequality for the invariant δ ( 2 , 2 ) for C C -totally real submanifolds in a normal complex contact space form and characterize the equality cases. We also prove the minimality of C C -totally real submanifolds of maximum dimension satisfying the equalities.

Smooth Boundary Values Along Totally Real Submanifolds

1984 ◽  
Vol 36 (2) ◽  
pp. 240-248 ◽  
Author(s):  
Edgar Lee Stout
Keyword(s):  
Pseudoconvex Domain ◽  
Smooth Boundary ◽  
Regularity Result ◽  
Boundary Values ◽  
Real Submanifolds ◽  
Strongly Pseudoconvex Domain ◽  
Real Submanifold ◽  
Totally Real Submanifold ◽  
Class C ◽  
Totally Real

The main result of this paper is the following regularity result:THEOREM. Let D ⊂ CNbe a bounded, strongly pseudoconvex domain with bD of class Ck, k ≧ 3. Let Σ ⊂ bD be an N-dimensional totally real submanifold, and let f ∊ A(D) satisfy |f| = 1 on Σ, |f| < 1 on. If Σ is of class Cr, 3 ≦ r < k, then the restriction fΣ = f|Σ of f to Σ is of class Cr − 0, and if Σ is of class Ck, then fΣ is of class Ck − 1.Here, of course, A(D) denotes the usual space of functions continuous on , holomorphic on D, and we shall denote by Ak(D), k = 1, 2, …, the space of functions holomorphic on D whose derivatives or order k lie in A(D).

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