| Title: | THEOREMS OF EXISTENCE OF LOCAL AND GLOBAL SOLUTIONS OF PDEs IN THE CATEGORY OF NONCOMMUTATIVE QUATERNIONIC MANIFOLDS |
| DOI No: | 10.1142/9789812810038_0021 |
| Source: | QUATERNIONIC STRUCTURES IN MATHEMATICS AND PHYSICS (pp 329-337)
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| Author(s): | AGOSTINO PRÁSTARO
Università di Roma "La Sapienza", Via A.Scarpa, 16 - 00161 Roma, Italy
Dipartimento di Metodi e Modelli Matematici per le Scienze Applicate, Via A.Scarpa, 16 - 00161 Roma, Italy
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| Abstract: | In this paper we apply our recent geometric theory of noncommutative (quantum) manifolds and noncommutative (quantum) PDEs [7,8,12] to the category of quantum quaternionic manifolds. These are manifolds modelled on spaces built starting from quaternionic algebras. For PDEs considered in such category we determine theorems of existence of local and global quantum quaternionic solutions. We shaw also that such a category of quantum quaternionic manifolds properly contains that of manifolds with (almost) quaternionic structure. So our theorems of existence of quantum quaternionic manifolds for PDEs produce a cascade of new solutions with nontrivial topology. |
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