Paolo Piccinni
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Research Subjects
Paolo Piccinni has a total of 14 co-authors. Here are the top co-authors by number of shared publications:
- Maurizio Parton
University of Chieti-Pescara, Chieti, Italy
7 shared publications - Liviu Ornea
University of Bucharest
6 shared publications - Maurizio Parton
Dipartimento di Scienze, Universita di Chieti—Pescara, Pescara, Italy
6 shared publications - Victor Vuletescu
Faculty of Mathematics and Informatics, University of Bucharest, Bucharest, Romania
3 shared publications - Charles P. Boyer
University of New Mexico
2 shared publications - Krzysztof Galicki
University of New Mexico
2 shared publications
Latest Publications
- Open Access
- 8 December 2020
- Published by Springer Nature in Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg
- Vol. 91 (1) , 101-115
Clifford systems, Clifford structures, and their canonical differential forms
- 8 December 2020
- Published by Springer Nature in Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg
- Vol. 91 (1) , 101-115
Open AccessClifford systems, Clifford structures, and their canonical differential forms
- 16 March 2020
- Published by Springer Nature in Annals of Global Analysis and Geometry
- Vol. 57 (3) , 465-487
An even Clifford diamond
- 16 March 2020
- Published by Springer Nature in Annals of Global Analysis and Geometry
- Vol. 57 (3) , 465-487
An even Clifford diamond
- Open Access
- 1 January 2019
- Published by Walter de Gruyter GmbH in Complex Manifolds
- Vol. 6 (1) , 138-149
Parallelizations on products of spheres and octonionic geometry
A classical theoremof Kervaire states that products of spheres are parallelizable if and only if at least one of the factors has odd dimension. Two explicit parallelizations on Sm × S2h−1 seem to be quite natural, and have been previously studied by the first named author in [32]. The present paper is devoted to the three choices G = G2, Spin(7), Spin(9) of G-structures on Sm × S2h−1, respectively with m + 2h − 1 = 7, 8, 16 and related with octonionic geometry.
- 1 January 2019
- Published by Walter de Gruyter GmbH in Complex Manifolds
- Vol. 6 (1) , 138-149
Open AccessParallelizations on products of spheres and octonionic geometry
A classical theoremof Kervaire states that products of spheres are parallelizable if and only if at least one of the factors has odd dimension. Two explicit parallelizations on Sm × S2h−1 seem to be quite natural, and have been previously studied by the first named author in [32]. The present paper is devoted to the three choices G = G2, Spin(7), Spin(9) of G-structures on Sm × S2h−1, respectively with m + 2h − 1 = 7, 8, 16 and related with octonionic geometry.
- Open Access
The Role of Spin(9) in Octonionic Geometry
Starting from the 2001 Thomas Friedrich's work on Spin(9), we review some interactions between Spin(9) and geometries related to octonions. Several topics are discussed in this respect: explicit descriptions of the Spin(9) canonical 8-form and its analogies with quaternionic geometry as well as the role of Spin(9) both in the classical problems of vector fields on spheres and in the geometry of the octonionic Hopf fibration. Next, we deal with locally conformally parallel Spin(9) manifolds in the framework of intrinsic torsion. Finally, we discuss applications of Clifford systems and Clifford structures to Cayley-Rosenfeld planes and to three series of Grassmannians.
Open AccessThe Role of Spin(9) in Octonionic Geometry
Starting from the 2001 Thomas Friedrich's work on Spin(9), we review some interactions between Spin(9) and geometries related to octonions. Several topics are discussed in this respect: explicit descriptions of the Spin(9) canonical 8-form and its analogies with quaternionic geometry as well as the role of Spin(9) both in the classical problems of vector fields on spheres and in the geometry of the octonionic Hopf fibration. Next, we deal with locally conformally parallel Spin(9) manifolds in the framework of intrinsic torsion. Finally, we discuss applications of Clifford systems and Clifford structures to Cayley-Rosenfeld planes and to three series of Grassmannians.
- Open Access
The Role of Spin(9) in Octonionic Geometry
Starting from the 2001 Thomas Friedrich’s work on , we review some interactions between and geometries related to octonions. Several topics are discussed in this respect: explicit descriptions of the canonical 8-form and its analogies with quaternionic geometry as well as the role of both in the classical problems of vector fields on spheres and in the geometry of the octonionic Hopf fibration. Next, we deal with locally conformally parallel manifolds in the framework of intrinsic torsion. Finally, we discuss applications of Clifford systems and Clifford structures to Cayley–Rosenfeld planes and to three series of Grassmannians.Open AccessThe Role of Spin(9) in Octonionic Geometry
Starting from the 2001 Thomas Friedrich’s work on , we review some interactions between and geometries related to octonions. Several topics are discussed in this respect: explicit descriptions of the canonical 8-form and its analogies with quaternionic geometry as well as the role of both in the classical problems of vector fields on spheres and in the geometry of the octonionic Hopf fibration. Next, we deal with locally conformally parallel manifolds in the framework of intrinsic torsion. Finally, we discuss applications of Clifford systems and Clifford structures to Cayley–Rosenfeld planes and to three series of Grassmannians. - 1 August 2018
- Published by Elsevier in Differential Geometry and its Applications
- Vol. 59, 122-137
On some Grassmannians carrying an even Clifford structure
- 1 August 2018
- Published by Elsevier in Differential Geometry and its Applications
- Vol. 59, 122-137
On some Grassmannians carrying an even Clifford structure
- Open Access
On some Grassmannians carrying an even Clifford structure
We give an explicit description of the non-flat parallel even Clifford structures of rank 8, 6, 5 on some real, complex and quaternionic Grassmannians, and discuss the r\^ole of the octonions in them, in particular for some low dimensional examples.
Open AccessOn some Grassmannians carrying an even Clifford structure
We give an explicit description of the non-flat parallel even Clifford structures of rank 8, 6, 5 on some real, complex and quaternionic Grassmannians, and discuss the r\^ole of the octonions in them, in particular for some low dimensional examples.
- 23 September 2017
- Published by Springer Nature
- p. 291-305
On the Cohomology of Some Exceptional Symmetric Spaces
- 23 September 2017
- Published by Springer Nature
- p. 291-305
On the Cohomology of Some Exceptional Symmetric Spaces
- Open Access
On the cohomology of some exceptional symmetric spaces
This is a survey on the construction of a canonical or "octonionic K\"ahler" 8-form, representing one of the generators of the cohomology of the four Cayley-Rosenfeld projective planes. The construction, in terms of the associated even Clifford structures, draws a parallel with that of the quaternion K\"ahler 4-form. We point out how these notions allow to describe the primitive Betti numbers with respect to different even Clifford structures, on most of the exceptional symmetric spaces of compact type.
Open AccessOn the cohomology of some exceptional symmetric spaces
This is a survey on the construction of a canonical or "octonionic K\"ahler" 8-form, representing one of the generators of the cohomology of the four Cayley-Rosenfeld projective planes. The construction, in terms of the associated even Clifford structures, draws a parallel with that of the quaternion K\"ahler 4-form. We point out how these notions allow to describe the primitive Betti numbers with respect to different even Clifford structures, on most of the exceptional symmetric spaces of compact type.
- Open Access
Clifford systems in octonionic geometry
We give an inductive construction for irreducible Clifford systems on Euclidean vector spaces. We then discuss how this notion can be adapted to Riemannian manifolds, and outline some developments in octonionic geometry.
Open AccessClifford systems in octonionic geometry
We give an inductive construction for irreducible Clifford systems on Euclidean vector spaces. We then discuss how this notion can be adapted to Riemannian manifolds, and outline some developments in octonionic geometry.