scholarly journals Totally real submanifolds of a quaternionic Kaehlerian manifold

1978 ◽  
Vol 29 (3) ◽  
pp. 261-270 ◽  
Author(s):  
Shōichi Funabashi
Keyword(s):  
Real Submanifolds ◽  
Totally Real ◽  
Kaehlerian Manifold

On Totally Real Submanifolds in a 6-Sphere

1990 ◽  
Vol 33 (2) ◽  
pp. 162-166
Author(s):  
M. A. Bashir
Keyword(s):  
Complex Structure ◽  
Dimensional Sphere ◽  
Almost Complex Structure ◽  
Real Submanifolds ◽  
Cayley Algebra ◽  
Almost Complex ◽  
Real Submanifold ◽  
Totally Real Submanifold ◽  
Totally Real ◽  
Kaehlerian Manifold

AbstractThe 6-dimensional sphere S6 has an almost complex structure induced by properties of Cayley algebra. With respect to this structure S6 is a nearly Kaehlerian manifold. We investigate 2-dimensional totally real submanifolds in S6. We prove that a 2-dimensional totally real submanifold in S6 is flat.

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).

scholarly journals Characterizing a class of totally real submanifolds of $S^6$ by their sectional curvatures

1995 ◽  
Vol 47 (2) ◽  
pp. 185-198 ◽  
Author(s):  
Bang-Yen Chen ◽  
Franki Dillen ◽  
Leopold Verstraelen ◽  
Luc Vrancken
Keyword(s):  
Real Submanifolds ◽  
Sectional Curvatures ◽  
Totally Real
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