Rotational embeddings in $Bbb{E}^4$ with pointwise 1-type gauss map

BAYRAM, Bengü Kılıç; KIM, Young Ho; Bulca, Betul; ARSLAN, Kadri; OZTÜRK, GÜNAY

Rotational embeddings in $Bbb{E}^4$ with pointwise 1-type gauss map

Kadri ARSLAN, (Uludağ Üniversitesi, Fen Fakültesi, Matematik Bölümü, Bursa, Türkiye)

Betül BULCA, (Uludağ Üniversitesi, Fen Fakültesi, Matematik Bölümü, Bursa, Türkiye)

Bengü Kılıç BAYRAM, (Balıkesir Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü, Balıkesir, Türkiye)

Young Ho KIM, (Department of Mathematics Kyunpook National University Taegu, Korea)

Günay ÖZTÜRK (Kocaeli Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü, Kocaeli, Türkiye)

Turkish Journal of Mathematics

1 0

Yıl: 2011 Cilt: 35 Sayı: 3 Sayfa Aralığı: 493 - 499 Metin Dili: İngilizce İndeks Tarihi: 29-07-2022

Rotational embeddings in $Bbb{E}^4$ with pointwise 1-type gauss map

Öz:

In the present article we study the rotational embedded surfaces in $Bbb{E}^4$ . The rotational embedded surface was first studied by G. Ganchev and V. Milousheva as a surface in $Bbb{E}^4$ . The Otsuki (non-round) sphere in $Bbb{E}^4$ is one of the special examples of this surface. Finally, we give necessary and sufficient conditions for the flat Ganchev-Milousheva rotational surface to have pointwise 1-type Gauss map.

Anahtar Kelime:

Konular: Matematik

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık

[1] Baikoussis, C. and Blair, D. E.: On the Gauss map of ruled surfaces. Glasgow Math. J. 34, 355-359 (1992).
[2] Baikoussis, C., Chen, B. Y and Verstraelen, L.: Ruled surfaces and tubes with finite type Gauss map. Tokyo J. Math. 16, 341-349 (1993).
[3] Baikoussis, C. and Verstraelen, L.: On the Gauss map of helicoidal surfaces. Rend. Sem. Mat. Messina Ser. II 16, 31-42 (1993)
[4] Chen, B. Y.: Total mean curvature and submanifolds of finite type. Series in Pure Mathematics. 1. World Scientific Publishing Co. Singapore, (1984).
[5] Chen, B. Y.: Finite type submanifolds and generalizations. Universita degli Studi di Roma ”La Sapienza”, Dipartimento di Matematica. IV, 68 p. (1985).
[6] Chen, B. Y., Choi, M. and Kim, Y. H.: Surfaces of revolution with pointwise 1-type Gauss map. J. Korean Math. Soc. 42, no. 3, 447-455 (2005).
[7] Chen, B. Y. and Ishikawa, S.: On classification of some surfaces of revolution of finite type. Tsukuba J. Math. 17, no. 1, 287-298 (1993).
[8] Chen, B. Y. and Piccinni, P.: Submanifolds with finite type Gauss map. Bull. Austral. Math. Soc. 35, no. 2, 161-186 (1987).
[9] Choi, M. and Kim, Y. H.: Characterization of the helicoid as ruled surfaces with pointwise 1-type Gauss map. Bull. Korean Math. Soc. 38, no. 4, 753-761 (2001).
[10] Ganchev, G. and Milousheva, V.: On the theory of surfaces in the four-dimensional Euclidean space. Kodai Math. J. 31, 183-198 (2008).
[11] Kim, Y. H. and Yoon, D. W.: Ruled surfaces with finite type Gauss map in Minkowski spaces. Soochow J. Math. 26, no. 1, 85-96 (2000).
[12] Kim, Y. H. and Yoon, D. W.: Ruled surfaces with pointwise 1-type Gauss map. J. Geom. Phys. 34, no. 3-4, 191-205 (2000).
[13] Kim, Y. H. and Yoon, D. W.: On the Gauss map of ruled surfaces in Minkowski space. Rocky Mountain J. Math. 35, no. 5, 1555-1581 (2005).
[14] Seaman, W.: Helicoids of constant mean curvature and their Gauss maps. Pacific J. Math. 110, no. 2, 387-396 (1984).
[15] Yoon, D. W.: Rotation surfaces with finite type Gauss map in $Bbb {E}^ 4$. Indian J. Pure Appl. Math. 32(12), 1803-1808 (2001).
[16] Yoon, D. W.: Some properties of the Clifford torus as rotation surface. Indian J. Pure Appl. Math. 34(6), 907-915 (2003).

APA	ARSLAN K, Bulca B, BAYRAM B, KIM Y, OZTÜRK G (2011). Rotational embeddings in $Bbb{E}^4$ with pointwise 1-type gauss map. , 493 - 499.
Chicago	ARSLAN Kadri,Bulca Betul,BAYRAM Bengü Kılıç,KIM Young Ho,OZTÜRK GÜNAY Rotational embeddings in $Bbb{E}^4$ with pointwise 1-type gauss map. (2011): 493 - 499.
MLA	ARSLAN Kadri,Bulca Betul,BAYRAM Bengü Kılıç,KIM Young Ho,OZTÜRK GÜNAY Rotational embeddings in $Bbb{E}^4$ with pointwise 1-type gauss map. , 2011, ss.493 - 499.
AMA	ARSLAN K,Bulca B,BAYRAM B,KIM Y,OZTÜRK G Rotational embeddings in $Bbb{E}^4$ with pointwise 1-type gauss map. . 2011; 493 - 499.
Vancouver	ARSLAN K,Bulca B,BAYRAM B,KIM Y,OZTÜRK G Rotational embeddings in $Bbb{E}^4$ with pointwise 1-type gauss map. . 2011; 493 - 499.
IEEE	ARSLAN K,Bulca B,BAYRAM B,KIM Y,OZTÜRK G "Rotational embeddings in $Bbb{E}^4$ with pointwise 1-type gauss map." , ss.493 - 499, 2011.
ISNAD	ARSLAN, Kadri vd. "Rotational embeddings in $Bbb{E}^4$ with pointwise 1-type gauss map". (2011), 493-499.

APA	ARSLAN K, Bulca B, BAYRAM B, KIM Y, OZTÜRK G (2011). Rotational embeddings in $Bbb{E}^4$ with pointwise 1-type gauss map. Turkish Journal of Mathematics, 35(3), 493 - 499.
Chicago	ARSLAN Kadri,Bulca Betul,BAYRAM Bengü Kılıç,KIM Young Ho,OZTÜRK GÜNAY Rotational embeddings in $Bbb{E}^4$ with pointwise 1-type gauss map. Turkish Journal of Mathematics 35, no.3 (2011): 493 - 499.
MLA	ARSLAN Kadri,Bulca Betul,BAYRAM Bengü Kılıç,KIM Young Ho,OZTÜRK GÜNAY Rotational embeddings in $Bbb{E}^4$ with pointwise 1-type gauss map. Turkish Journal of Mathematics, vol.35, no.3, 2011, ss.493 - 499.
AMA	ARSLAN K,Bulca B,BAYRAM B,KIM Y,OZTÜRK G Rotational embeddings in $Bbb{E}^4$ with pointwise 1-type gauss map. Turkish Journal of Mathematics. 2011; 35(3): 493 - 499.
Vancouver	ARSLAN K,Bulca B,BAYRAM B,KIM Y,OZTÜRK G Rotational embeddings in $Bbb{E}^4$ with pointwise 1-type gauss map. Turkish Journal of Mathematics. 2011; 35(3): 493 - 499.
IEEE	ARSLAN K,Bulca B,BAYRAM B,KIM Y,OZTÜRK G "Rotational embeddings in $Bbb{E}^4$ with pointwise 1-type gauss map." Turkish Journal of Mathematics, 35, ss.493 - 499, 2011.
ISNAD	ARSLAN, Kadri vd. "Rotational embeddings in $Bbb{E}^4$ with pointwise 1-type gauss map". Turkish Journal of Mathematics 35/3 (2011), 493-499.