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@article{Волкова_Смоленцев_2024, title={Параконтактные метрические структуры на пятимерных неразрешимых алгебрах Ли}, url={http://izvestiya.asu.ru/article/view/%282024%291-13}, DOI={10.14258/izvasu(2024)1-13}, abstractNote={<p style="text-align: justify; text-indent: 14.0pt;"><span class="font54">В данной работе исследован вопрос о существовании параконтактных метрических и парасасакие-вых структур на пятимерных неразрешимых алгебрах Ли. В соответствии с классификационными результатами A. Diatta существует три таких алгебры Ли. Это разложимые алгебры Ли <em>aff(</em></span><span class="font37"><em>K</em></span><span class="font54"><em>)xsl(2,</em></span><span class="font37"><em>K</em></span><span class="font54"><em>), aff(</em></span><span class="font37"><em>K</em></span><span class="font54"><em>)xso(3)</em> и неразложимая sl(2,</span><span class="font37">K</span><span class="font54">) x<sub>p</sub> </span><span class="font37">К</span><span class="font54"><sup>2</sup>, где <em>р</em> есть обычное действие sl(2,</span><span class="font37">K</span><span class="font54">) на </span><span class="font37">К</span><span class="font54"><sup>2</sup>. Разложимые алгебры Ли являются прямыми произведениями точной сим-плектической алгебры Ли <em>aff(</em></span><span class="font37"><em>K</em></span><span class="font54"><em>)</em> и трехмерных контактных алгебр Ли. Для неразложимой алгебры Ли sl(2,</span><span class="font37">K</span><span class="font54">) х<sub>р</sub> </span><span class="font37">К</span><span class="font54"><sup>2</sup> в работе Diatta указана процедура построения контактной структуры. Каждая алгебра Ли рассмотрена подробно. Показано, что только на <em>aff(</em></span><span class="font37"><em>K</em></span><span class="font54"><em>)</em> х sl(2,</span><span class="font37">K</span><span class="font54">) существуют парасасакиевы структуры. Найдены их выражения в явном виде, вычислены тензоры Риччи и скалярные кривизны. Для других алгебр Ли <em>aff(</em></span><span class="font37"><em>K</em></span><span class="font54"><em>)xso(3)</em> и sl(2,</span><span class="font37">K</span><span class="font54">) х<sub>р</sub> </span><span class="font37">К</span><span class="font54"><sup>2</sup> показано, что существуют параконтактные метрические структуры, но все они не обладают свойством K-параконтактности. Для указанных двух последних алгебр Ли приведены примеры параконтактных метрических структур.</span></p>}, number={1(135)}, journal={Известия Алтайского государственного университета}, author={Волкова, Анастасия Александровна and Смоленцев, Николай Константинович}, year={2024}, month={апр.}, pages={95-100} }