Dergiler / Mathematical Sciences and Applications E-Notes / 2013 / Cilt: 1 Sayı: 1
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- Sayfa
- 18–35
- DOI
- —
Özet
❧✐❦❡ ❤②♣❡rs✉❡r❢❛❝❡s✳ ❙❡❝t✐♦♥ ✸ ✐♥tr♦❞✉❝❡s ❛ss♦❝✐❛t❡ ♠❡tr✐❝ t♦ ❛ ♥♦r♠❛❧✐③❡❞ ❧✐❣❤t❧✐❦❡ ❤②♣❡rs✉r❢❛❝❡ t❤r♦✉❣❤ ♣s❡✉❞♦✲✐♥✈❡rs✐♦♥ ♦❢ ❞❡❣❡♥❡r❛t❡ ♠❡tr✐❝s ❛♥❞ s❡❝t✐♦♥ ✹ ❞❡❛❧s ✇✐t❤ t❤❡ ❞❡t❡r♠✐♥❛♥t ♦❢ t❤❡ ❛ss♦❝✐❛t❡ ♠❡tr✐❝ r❡❧❛t✐✈❡ t♦ t❤❡ ✐♥❞✉❝❡❞ ✈♦❧✉♠❡ ❡❧❡♠❡♥t✳ ■♥ s❡❝t✐♦♥ ✺ ✇❡ ♣r❡s❡♥t ❛ t❡❝❤♥✐❝❛❧ ❧❡♠♠❛ ❛❝❝♦✉♥t✐♥❣ ♦♥ ❤♦✇ ✐♥❞✉❝❡❞ ❣❡♦♠❡tr✐❝ ♦❜❥❡❝ts ❝❤❛♥❣❡ ✉♥❞❡r ❝❤❛♥❣❡ ✐♥ ♥♦r♠❛❧✐③❛t✐♦♥ ❢♦❧❧♦✇❡❞ ❜② ❛ ❝♦♠♣❛t✐❜✐❧✐t② r❡s✉❧t ♥❡❡❞❡❞ ✐♥ t❤❡ ❢♦r♠✉❧❛t✐♦♥ ♦❢ ♦✉r ♥♦r♠❛❧✐③❛t✐♦♥ ❝♦♥str❛✐♥ts✳ ❚❤❡r❡❛❢t❡r✱ ✇❡ ❝♦♥s✐❞❡r ✐♥ s❡❝t✐♦♥ ✻ t❤❡ ✐♥✈❛r✐❛♥t ♥♦r♠❛❧✐③✐♥❣ ❞✐✛❡r❡♥t✐❛❧ ❡q✉❛t✐♦♥ ❛♥❞ ✐♥tr♦❞✉❝❡ ✐♥ s❡❝t✐♦♥ ✼ t❤❡ ❝❛❧✐❜r❛t❡❞ ❞✐✈❡r❣❡♥❝❡ ♦❢ s❡❝t✐♦♥s ❛❧♦♥❣ t❤❡ ♥✉❧❧ ❤②♣❡rs✉❡r❢❛❝❡s✳ ❋✐♥❛❧❧②✱ ✇❡ ♣r❡s❡♥t t❤❡ ♠❛✐♥ r❡s✉❧t ✐♥ s❡❝t✐♦♥ ✽ ❢♦❧❧♦✇❡❞ ❜② ❛ ❜❛s✐❝ ❡①❛♠♣❧❡ ♦♥ t❤❡ ♥✉❧❧ ❝♦♥❡ ∧3⊂ R4✳
Abstract
We show that on a non-minimal lightlike hypersurface with nullity degree 1, there exists a unique null transversal (normalizing) vector eld with prescribed calibrated divergence, for which the induced connection and the LeviCivita connection of the associate non-degenerate metric coincide.