On the composition and  exterior products of double forms and ppp-pure manifolds

Abdelhadi BELKHIRAT; Mohammed LABBI

Makale detayları

On the composition and exterior products of double forms and ppp-pure manifolds

Yazarlar:

Abdelhadi BELKHIRAT | Mohammed LABBI

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2019 Vol.43 Issue 1, pp.539-560

Belge Tipi:

Makale

Yayın Tarihi:

1/2019

Belge Dili:

Türkçe

Document ID (Org No.):

2000745711

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098

Özet:

 

We translate into double forms formalism the basic Greub and Greub-Vanstone identities that were previously obtained  in  mixed exterior algebras. In particular, we  introduce a second product in the space of double forms, namely the composition product, which provides this space with a second associative algebra structure. The composition product interacts with the exterior product of double forms; we show that the resulting relations provide simple  alternative proofs to  some classical   linear algebra identities as well as  to recent results in the exterior algebra of double forms. We define and study a refinement of the notion of pure curvature of  Maillot, namely ppp-pure curvature,  and  we use one of the basic identities to prove that if a Riemannian nnn-manifold has kkk-pure curvature  and n≥4kn≥4kn\geq 4k  then its Pontryagin class of degree 4k4k4k vanishes.

Makale detayları

On the composition and exterior products of double forms and ppp-pure manifolds

Yazarlar: Abdelhadi BELKHIRAT | Mohammed LABBI

Yayıncı: TUBITAK

Dergi: Turkish Journal of Mathematics 2019 Vol.43 Issue 1, pp.539-560

Belge Tipi: Makale

Yayın Tarihi: 1/2019

Belge Dili: Türkçe

Document ID (Org No.): 2000745711

Sıklık: İki Aylık

eISSN: 1303-6149

pISSN: 1300-0098

Sayı

Yazarlar:

Abdelhadi BELKHIRAT | Mohammed LABBI

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2019 Vol.43 Issue 1, pp.539-560

Belge Tipi:

Makale

Yayın Tarihi:

1/2019

Belge Dili:

Türkçe

Document ID (Org No.):

2000745711

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098