Applications of the Golden Ratio on Riemannian Manifolds

Cristina-elena HRETCANU

Makale detayları

Applications of the Golden Ratio on Riemannian Manifolds

Yazarlar:

Cristina-elena HRETCANU

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2009 Vol.33 Issue 2, pp.179-191

Belge Tipi:

Makale

Yayın Tarihi:

1/2009

Belge Dili:

Türkçe

Document ID (Org No.):

2000748246

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098

Anahtar kelimeler:

Özet:

 

The Golden Ratio is a fascinating topic that continually  generates new ideas.  The main purpose of the present paper is to  point out and find some applications of the Golden Ratio and of  Fibonacci numbers in Differential Geometry.  We study a structure  defined on a class of Riemannian manifolds, called by us a Golden  Structure.  A Riemannian manifold endowed with a Golden Structure will  be called a Golden Riemannian manifold.  Precisely, we say that an  (1,1)-tensor field \widetilde{P} on a m-dimensional Riemannian  manifold (\widetilde{M}, \widetilde{g}) is a Golden Structure if it  satisfies the equation \widetilde{P}2=\widetilde{P}+I (which is  similar to that satisfied by the Golden Ratio f) where I stands for  the (1,1) identity tensor field.  First, we establish several  properties of the Golden Structure.  Then we show that a Golden  Structure induces on every invariant submanifold a Golden Structure,  too.  This fact is illustrated on a product of spheres in an Euclidean  space.

 

The Golden Ratio is a fascinating topic that continually  generates new ideas.  The main purpose of the present paper is to  point out and find some applications of the Golden Ratio and of  Fibonacci numbers in Differential Geometry.  We study a structure  defined on a class of Riemannian manifolds, called by us a Golden  Structure.  A Riemannian manifold endowed with a Golden Structure will  be called a Golden Riemannian manifold.  Precisely, we say that an  (1,1)-tensor field \widetilde{P} on a m-dimensional Riemannian  manifold (\widetilde{M}, \widetilde{g}) is a Golden Structure if it  satisfies the equation \widetilde{P}2=\widetilde{P}+I (which is  similar to that satisfied by the Golden Ratio f) where I stands for  the (1,1) identity tensor field.  First, we establish several  properties of the Golden Structure.  Then we show that a Golden  Structure induces on every invariant submanifold a Golden Structure,  too.  This fact is illustrated on a product of spheres in an Euclidean  space.

Makale detayları

Applications of the Golden Ratio on Riemannian Manifolds

Yazarlar:

Cristina-elena HRETCANU

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2009 Vol.33 Issue 2, pp.179-191

Belge Tipi:

Makale

Yayın Tarihi:

1/2009

Belge Dili:

Türkçe

Document ID (Org No.):

2000748246

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098

Riemannian manifold

Golden Structure

induced structures on submanifolds

Golden Ratio

Sayı

Makale detayları

Applications of the Golden Ratio on Riemannian Manifolds

Yazarlar: Cristina-elena HRETCANU

Yayıncı: TUBITAK

Dergi: Turkish Journal of Mathematics 2009 Vol.33 Issue 2, pp.179-191

Belge Tipi: Makale

Yayın Tarihi: 1/2009

Belge Dili: Türkçe

Document ID (Org No.): 2000748246

Sıklık: İki Aylık

eISSN: 1303-6149

pISSN: 1300-0098

Riemannian manifold

Golden Structure

induced structures on submanifolds

Golden Ratio

Sayı

Yazarlar:

Cristina-elena HRETCANU

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2009 Vol.33 Issue 2, pp.179-191

Belge Tipi:

Makale

Yayın Tarihi:

1/2009

Belge Dili:

Türkçe

Document ID (Org No.):

2000748246

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098