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DTSTART:20230312T070000
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DTSTART:20221106T060000
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DTSTART;TZID=America/Toronto:20230323T143000
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URL:https://uwaterloo.ca/pure-mathematics-geometry-topology/events/some-asp
 ects-geometry-unit-vector-fields
SUMMARY:Some aspects of geometry of unit vector fields
CLASS:PUBLIC
DESCRIPTION:ALEXANDER YAMPOLSKY\, V.N. KARAZIN NATIONAL UNIVERSITY\, KHAR
 KIV\,\nUKRAINE\n\nA vector field ξ on a Riemannian manifold (_M\,g_) de
 fines a mapping\nξ:  _M_→_TM_ (or ξ: _M_→_T_1_M_ in case of |
 ξ|= 1).\nEndowing _TM_ with the Sasaki metric gives rise to the Riemann
 ian\nmetric on ξ(_M_) ⊂ _TM_ or ξ(_M_) ⊂ _T_1_M_\, respectively
 .\nThis idea allows to assign the geometric properties from the geometry\n
 of submanifolds to the vector field. So\, one can talk about the\nintrins
 ic or extrinsic geometry of vector fields.\n\nThe most developed idea in 
 a given setting is the idea of harmonic and\nminimal unit vector fields. 
 The report outlines the geometry of unit\nvector fields focused on exampl
 es\nof MINIMAL\, HARMONIC and TOTALLY GEODESIC properties. Mean\ncurv
 ature of the Reeb vector field on (_α\,β_) - trans-Sasakian\nmanifold w
 ill be presented as well as its minimality and total\ngeodesity conditions
 . The properties of invariant unit vector fields\non the oscillator Lie g
 roup will be considered in more detail.\n\nMC 5417
DTSTAMP:20260319T011656Z
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