Öz 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 $p$-pure curvature, and we use one of the basic identities to prove that if a Riemannian $n$-manifold has $k$-pure curvature and $n\geq 4k$ then its Pontryagin class of degree $4k$ vanishes.

Anahtar Kelimeler:
## Composition product of double forms, exterior product of double forms, interior product of a double form, mixed exterior algebra, Pontrjagin form, Pontrjagin number, $p$-pure curvature tensor

Bibtex | `@ { tbtkmath575283, journal = {Turkish Journal of Mathematics}, issn = {1300-0098}, eissn = {1303-6149}, address = {}, publisher = {TÜBİTAK}, year = {2019}, volume = {43}, pages = {539 - 560}, doi = {}, title = {On the composition and exterior products of double forms and \$p\$-pure manifolds}, key = {cite}, author = {Belkhırat, Abdelhadi and Labbı, Mohammed} }` |

APA | Belkhırat, A , Labbı, M . (2019). On the composition and exterior products of double forms and $p$-pure manifolds . Turkish Journal of Mathematics , 43 (1) , 539-560 . |

MLA | Belkhırat, A , Labbı, M . "On the composition and exterior products of double forms and $p$-pure manifolds" . Turkish Journal of Mathematics 43 (2019 ): 539-560 < |

Chicago | Belkhırat, A , Labbı, M . "On the composition and exterior products of double forms and $p$-pure manifolds". Turkish Journal of Mathematics 43 (2019 ): 539-560 |

RIS | TY - JOUR T1 - On the composition and exterior products of double forms and $p$-pure manifolds AU - Abdelhadi Belkhırat , Mohammed Labbı Y1 - 2019 PY - 2019 N1 - DO - T2 - Turkish Journal of Mathematics JF - Journal JO - JOR SP - 539 EP - 560 VL - 43 IS - 1 SN - 1300-0098-1303-6149 M3 - UR - Y2 - 2021 ER - |

EndNote | %0 Turkish Journal of Mathematics On the composition and exterior products of double forms and $p$-pure manifolds %A Abdelhadi Belkhırat , Mohammed Labbı %T On the composition and exterior products of double forms and $p$-pure manifolds %D 2019 %J Turkish Journal of Mathematics %P 1300-0098-1303-6149 %V 43 %N 1 %R %U |

ISNAD | Belkhırat, Abdelhadi , Labbı, Mohammed . "On the composition and exterior products of double forms and $p$-pure manifolds". Turkish Journal of Mathematics 43 / 1 (Şubat 2019): 539-560 . |

AMA | Belkhırat A , Labbı M . On the composition and exterior products of double forms and $p$-pure manifolds. Turkish Journal of Mathematics. 2019; 43(1): 539-560. |

Vancouver | Belkhırat A , Labbı M . On the composition and exterior products of double forms and $p$-pure manifolds. Turkish Journal of Mathematics. 2019; 43(1): 539-560. |

IEEE | A. Belkhırat ve M. Labbı , "On the composition and exterior products of double forms and $p$-pure manifolds", Turkish Journal of Mathematics, c. 43, sayı. 1, ss. 539-560, Şub. 2019 |

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