scholarly journals Totally real minimal immersions of $n$-dimensional real space forms into $n$-dimensional complex space forms

1982 ◽  
Vol 84 (2) ◽  
pp. 243-243
Author(s):  
Norio Ejiri
Keyword(s):  
Complex Space ◽  
Real Space ◽  
Space Forms ◽  
Real Space Forms ◽  
Minimal Immersions ◽  
Complex Space Forms ◽  
Totally Real

Isotropic Immersions with Low Codimension of Complex Space Forms into Real Space Forms

2004 ◽  
Vol 47 (4) ◽  
pp. 492-503
Author(s):  
Nobutaka Boumuki
Keyword(s):  
Complex Space ◽  
Real Space ◽  
Space Forms ◽  
Real Space Forms ◽  
Complex Space Forms

AbstractThe main purpose of this paper is to determine isotropic immersions of complex space forms into real space forms with low codimension. This is an improvement of a result of S. Maeda.

Indefinite rigidity of complex submanifolds and maximal surfaces

1989 ◽  
Vol 106 (3) ◽  
pp. 481-494 ◽  
Author(s):  
Kinetsu Abe ◽  
Martin A. Magid
Keyword(s):  
Minimal Surfaces ◽  
Complex Space ◽  
Real Space ◽  
Rigidity Theorem ◽  
Space Forms ◽  
Maximal Surfaces ◽  
Real Space Forms ◽  
Complex Submanifolds ◽  
Complex Space Forms

In 1953, Calabi proved a rigidity theorem for Kählerian submanifolds in complex space forms [3]. The Calabi rigidity theorem, since then, has been successfully applied to various areas in geometry. Among them is the study of minimal surfaces in real space forms; see [4] for example.

scholarly journals ON ISOMETRIC MINIMAL IMMERSIONS FROM WARPED PRODUCTS INTO REAL SPACE FORMS

2002 ◽  
Vol 45 (3) ◽  
pp. 579-587 ◽  
Author(s):  
Bang-Yen Chen
Keyword(s):  
Euclidean Space ◽  
Warped Product ◽  
Minimal Immersion ◽  
Real Space ◽  
Sharp Inequality ◽  
Warping Function ◽  
Warped Products ◽  
Space Forms ◽  
Real Space Forms ◽  
Minimal Immersions

AbstractWe establish a general sharp inequality for warped products in real space form. As applications, we show that if the warping function $f$ of a warped product $N_1\times_fN_2$ is a harmonic function, then(1) every isometric minimal immersion of $N_1\times_fN_2$ into a Euclidean space is locally a warped-product immersion, and(2) there are no isometric minimal immersions from $N_1\times_f N_2$ into hyperbolic spaces.Moreover, we prove that if either $N_1$ is compact or the warping function $f$ is an eigenfunction of the Laplacian with positive eigenvalue, then $N_1\times_f N_2$ admits no isometric minimal immersion into a Euclidean space or a hyperbolic space for any codimension. We also provide examples to show that our results are sharp.AMS 2000 Mathematics subject classification: Primary 53C40; 53C42; 53B25

Horizontal Newton operators and high-order Minkowski formula

2020 ◽  
pp. 2050004
Author(s):  
Chiara Guidi ◽  
Vittorio Martino
Keyword(s):  
Complex Space ◽  
Space Form ◽  
Real Space ◽  
Second Fundamental Form ◽  
Space Forms ◽  
Nonlinear Operators ◽  
The Second Fundamental Form ◽  
Real Space Forms ◽  
Newton Transformations ◽  
Minkowski Formula

In this paper, we study the horizontal Newton transformations, which are nonlinear operators related to the natural splitting of the second fundamental form for hypersurfaces in a complex space form. These operators allow to prove the classical Minkowski formulas in the case of real space forms: unlike the real case, the horizontal ones are not divergence-free. Here, we consider the highest order of nonlinearity and we will show how a Minkowski-type formula can be obtained in this case.

Sign in / Sign up

Export Citation Format

Share Document