The Center Map of an Affine Immersion

2006 ◽  
Vol 49 (3-4) ◽  
pp. 201-217 ◽  
Author(s):  
Hitoshi Furuhata ◽  
Luc Vrancken
Keyword(s):  
Affine Immersion ◽  
Center Map

scholarly journals Centroaffine immersions of codimension two and projective hypersurface theory

1993 ◽  
Vol 132 ◽  
pp. 63-90 ◽  
Author(s):  
Katsumi Nomizu ◽  
Takeshi Sasaki
Keyword(s):  
Differential Geometry ◽  
Vector Field ◽  
Affine Connection ◽  
Affine Differential Geometry ◽  
Dimensional Manifold ◽  
Affine Immersion ◽  
Projective Hypersurface ◽  
Starting Point ◽  
Affine Immersions ◽  
Transversal Vector Field

Affine differential geometry developed by Blaschke and his school [B] has been reorganized in the last several years as geometry of affine immersions. An immersion f of an n-dimensional manifold M with an affine connection ∇ into an (n + 1)-dimensional manifold Ḿwith an affine connection ∇ is called an affine immersion if there is a transversal vector field ξ such that ∇xf*(Y) = f*(∇xY) + h(X,Y)ξ holds for any vector fields X, Y on Mn. When f: Mn→ Rn+1 is a nondegenerate hypersurface, there is a uniquely determined transversal vector field ξ, called the affine normal field, an essential starting point in classical affine differential geometry. The new point of view allows us to relax the non-degeneracy condition and gives us more freedom in choosing ξ; what this new viewpoint can accomplish in relating affine differential geometry to Riemannian geometry and projective differential geometry can be seen from [NP1], [NP2], [NS] and others. For the definitions and basic formulas on affine immersions, centroaffine immersions, conormal (or dual) maps, projective flatness, etc., the reader is referred to [NP1]. These notions will be generalized to codimension 2 in this paper.

Blaschke structure for a special affine immersion

2008 ◽  
Vol 43 (4) ◽  
pp. 214-220
Author(s):  
M. Faghfouri ◽  
A. Haji Badali ◽  
E. Pourreza
Keyword(s):  
Affine Immersion

scholarly journals Identifikasi Jumlah dan Faktor Timbulan Sampah Di Kawasan Wisata Malioboro

2020 ◽  
Vol 5 (1) ◽  
pp. 39-52
Author(s):  
Difla Nadjih ◽  
Sujarwo Saputro ◽  
Mukhlas Madani
Keyword(s):  
Rational Approach ◽  
Maximum Volume ◽  
Street Vendors ◽  
Daily Amount ◽  
Cigarette Butts ◽  
Plastic Bags ◽  
Food And Beverage ◽  
Negative Impacts ◽  
Center Map ◽  
Beverage Packaging

In preparing Malioboro as a 24-hour tourist area, garbage and waste can cause negative impacts. This study aims to identify the daily amount and factors of waste in the study area, namely the gate of Kepatihan sayap Malioboro area, using a phenomenological and rational approach. In this study, following the thoughts of B. Sommer (1980) about the person center map and place center map so that the movement of Malioboro visitors and the activities of visitors and street vendors in a certain period with a certain study area. The types of waste that most often appear are food and beverage packaging, plastic bags, plastic straws and cigarette butts. The maximum volume of waste that can be accommodated in the trash per day is 3 x 1.458 m3 = 4,374 m3 per day. Awareness of the importance of cleanliness is important through socialization in the form of a flash mob. The next suggestion is to maximize the function of the trash can by separating it according to its type.

scholarly journals On the geometry of affine Kähler immersions

1990 ◽  
Vol 120 ◽  
pp. 205-222 ◽  
Author(s):  
Katsumi Nomizu ◽  
Ulrich Pinkall ◽  
Fabio Podestà
Keyword(s):  
Isometric Immersion ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Complex Manifolds ◽  
Affine Immersion ◽  
Holomorphic Affine ◽  
Affine Immersions ◽  
Holomorphic Affine Immersion

In this paper we extend the work on affine immersions [N-Pi]-1 to the case of affine immersions between complex manifolds and lay the foundation for the geometry of affine Kähler immersions. The notion of affine Kähler immersion extends that of a holomorphic and isometric immersion between Kähler manifolds and can be contrasted to the notion of holomorphic affine immersion which has been established in the work of Dillen, Vrancken and Verstraelen [D-V-V] and that of Abe [A].

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