Some remarks on the moment curves in R4 and R3

Mircea Crasmareanu

Makale detayları

Some remarks on the moment curves in R4 and R3

Yazarlar:

Mircea Crasmareanu

Yayıncı:

Istanbul University

Ana Başlıklar:

Pure Mathematics (Other)

Dergi:

Istanbul Journal of Mathematics Vol.3 Issue 1, pp.34-38

Belge Tipi:

Makale

Yayın Tarihi:

6/2025

Belge Dili:

İngilizce

Document ID (Org No.):

2001355938

pISSN:

2980-3020

Anahtar kelimeler:

Özet:

 The moment curves and their normalizations are key tools in obtaining the famous Kac formula from the theory of random polynomials. We study here the normalized moment curves Γ   in the low dimensions  where  is the Euclidean  dimensional unit sphere; more precisely we consider   3 and   2. First, we compute the image of the normalized moment curve Γ3 under the well-known Hopf fibre map and show that this remarkable map reduces the length of Γ3. Second, we analyze the curve Γ2 using the theory of spherical Legendre curves. An image of Γ2 is included.

 The moment curves and their normalizations are key tools in obtaining the famous Kac formula from the theory of random polynomials. We study here the normalized moment curves Γ   in the low dimensions  where  is the Euclidean  dimensional unit sphere; more precisely we consider   3 and   2. First, we compute the image of the normalized moment curve Γ3 under the well-known Hopf fibre map and show that this remarkable map reduces the length of Γ3. Second, we analyze the curve Γ2 using the theory of spherical Legendre curves. An image of Γ2 is included.

 The moment curves and their normalizations are key tools in obtaining the famous Kac formula from the theory of random polynomials. We study here the normalized moment curves Γ   in the low dimensions  where  is the Euclidean  dimensional unit sphere; more precisely we consider   3 and   2. First, we compute the image of the normalized moment curve Γ3 under the well-known Hopf fibre map and show that this remarkable map reduces the length of Γ3. Second, we analyze the curve Γ2 using the theory of spherical Legendre curves. An image of Γ2 is included.

 The moment curves and their normalizations are key tools in obtaining the famous Kac formula from the theory of random polynomials. We study here the normalized moment curves Γ   in the low dimensions  where  is the Euclidean  dimensional unit sphere; more precisely we consider   3 and   2. First, we compute the image of the normalized moment curve Γ3 under the well-known Hopf fibre map and show that this remarkable map reduces the length of Γ3. Second, we analyze the curve Γ2 using the theory of spherical Legendre curves. An image of Γ2 is included.

Makale detayları

Some remarks on the moment curves in R4 and R3

Yazarlar:

Mircea Crasmareanu

Yayıncı:

Istanbul University

Ana Başlıklar:

Pure Mathematics (Other)

Dergi:

Istanbul Journal of Mathematics Vol.3 Issue 1, pp.34-38

Belge Tipi:

Makale

Yayın Tarihi:

6/2025

Belge Dili:

İngilizce

Document ID (Org No.):

2001355938

pISSN:

2980-3020

moment curve

Hopf map

spherical curve

Sayı

Makale detayları

Some remarks on the moment curves in R4 and R3

Yazarlar: Mircea Crasmareanu

Yayıncı: Istanbul University

Ana Başlıklar: Pure Mathematics (Other)

Dergi: Istanbul Journal of Mathematics Vol.3 Issue 1, pp.34-38

Belge Tipi: Makale

Yayın Tarihi: 6/2025

Belge Dili: İngilizce

Document ID (Org No.): 2001355938

pISSN: 2980-3020

moment curve

Hopf map

spherical curve

Sayı

Yazarlar:

Mircea Crasmareanu

Yayıncı:

Istanbul University

Ana Başlıklar:

Pure Mathematics (Other)

Dergi:

Istanbul Journal of Mathematics Vol.3 Issue 1, pp.34-38

Belge Tipi:

Makale

Yayın Tarihi:

6/2025

Belge Dili:

İngilizce

Document ID (Org No.):

2001355938

pISSN:

2980-3020