The new expressions of Gaussian curvature at spacelike congruences

ÇALIŞKAN, A.; KILIÇ, Ö.; UĞURLU, H. H.

The new expressions of Gaussian curvature at spacelike congruences

H. H. UĞURLU, (Celal Bayar Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü, Manisa, Türkiye)

A. ÇALIŞKAN, (Girilmedi)

Ö. KILIÇ (Girilmedi)

Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics

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Yıl: 2002 Cilt: 51 Sayı: 2 Sayfa Aralığı: 19 - 23 Metin Dili: İngilizce İndeks Tarihi: 29-07-2022

The new expressions of Gaussian curvature at spacelike congruences

Öz:

We obtained two fundamental formula in [1] for the geometry of spacelike congruences by means of dual hyperbolic and central angles. Beside we stated and proved the Manheim's, Liouville's and Hamilton's formulae. In this study we give the new expressions of the Gaussian curvature for the spacelike congruences by means of fundamental formulae.

Anahtar Kelime:

Konular: Matematik İstatistik ve Olasılık

Belge Türü: Makale Makale Türü: Diğer Erişim Türü: Erişime Açık

[l] Uğurlu, H. H., Çalışkan, A. and Kiliç, O., On the Geometry of Spacelike Congruences" Communications, Faculty of Sciences, University of Ankara, A1 Series,Vol. 50,(2001), 9-24.
[2] Uğurlu, H. H., On the Geometry of Timelike Surface" Communications , Faculty of Sciences, University of Ankara, A1 Series, 46 (1997) ??.
[3] Kılıç, O. and Çalışkan, A., The Frenet and Darboux Instantaneous Rotation Vectors for Curves on Spacelike Surface, Mathematical & Computational Applications, 1, (1996),149-157.

APA	UĞURLU H, ÇALIŞKAN A, KILIÇ Ö (2002). The new expressions of Gaussian curvature at spacelike congruences. , 19 - 23.
Chicago	UĞURLU H. H.,ÇALIŞKAN A.,KILIÇ Ö. The new expressions of Gaussian curvature at spacelike congruences. (2002): 19 - 23.
MLA	UĞURLU H. H.,ÇALIŞKAN A.,KILIÇ Ö. The new expressions of Gaussian curvature at spacelike congruences. , 2002, ss.19 - 23.
AMA	UĞURLU H,ÇALIŞKAN A,KILIÇ Ö The new expressions of Gaussian curvature at spacelike congruences. . 2002; 19 - 23.
Vancouver	UĞURLU H,ÇALIŞKAN A,KILIÇ Ö The new expressions of Gaussian curvature at spacelike congruences. . 2002; 19 - 23.
IEEE	UĞURLU H,ÇALIŞKAN A,KILIÇ Ö "The new expressions of Gaussian curvature at spacelike congruences." , ss.19 - 23, 2002.
ISNAD	UĞURLU, H. H. vd. "The new expressions of Gaussian curvature at spacelike congruences". (2002), 19-23.

APA	UĞURLU H, ÇALIŞKAN A, KILIÇ Ö (2002). The new expressions of Gaussian curvature at spacelike congruences. Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics, 51(2), 19 - 23.
Chicago	UĞURLU H. H.,ÇALIŞKAN A.,KILIÇ Ö. The new expressions of Gaussian curvature at spacelike congruences. Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics 51, no.2 (2002): 19 - 23.
MLA	UĞURLU H. H.,ÇALIŞKAN A.,KILIÇ Ö. The new expressions of Gaussian curvature at spacelike congruences. Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics, vol.51, no.2, 2002, ss.19 - 23.
AMA	UĞURLU H,ÇALIŞKAN A,KILIÇ Ö The new expressions of Gaussian curvature at spacelike congruences. Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics. 2002; 51(2): 19 - 23.
Vancouver	UĞURLU H,ÇALIŞKAN A,KILIÇ Ö The new expressions of Gaussian curvature at spacelike congruences. Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics. 2002; 51(2): 19 - 23.
IEEE	UĞURLU H,ÇALIŞKAN A,KILIÇ Ö "The new expressions of Gaussian curvature at spacelike congruences." Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics, 51, ss.19 - 23, 2002.
ISNAD	UĞURLU, H. H. vd. "The new expressions of Gaussian curvature at spacelike congruences". Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics 51/2 (2002), 19-23.