TY - JOUR
T1 - Conformal minimal surfaces immersed into HPn
AU - Chen, Xiaodong
AU - Jiao, Xiaoxiang
N1 - Publisher Copyright:
© 2017, Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag Berlin Heidelberg.
PY - 2017/12/1
Y1 - 2017/12/1
N2 - In this paper, we want to construct conformal minimal surfaces and conformal minimal two-spheres in HPn by the twistor map π: CP2 n + 1→ HPn. The construction is due to Eells and Wood’s conclusion about the composition of a horizontal harmonic map in 1983. Firstly, we give a characterization of horizontal holomorphic surfaces in CP5. Under this characterization, we construct eight families of conformal minimal surfaces in HP2. Then, we study horizontal Veronese sequences in CP4 and CP5, and we transform the construction into solving a quadratic equation. Based on this, we get some examples of conformal minimal two-spheres in HP2 with constant curvature 45 and 413.
AB - In this paper, we want to construct conformal minimal surfaces and conformal minimal two-spheres in HPn by the twistor map π: CP2 n + 1→ HPn. The construction is due to Eells and Wood’s conclusion about the composition of a horizontal harmonic map in 1983. Firstly, we give a characterization of horizontal holomorphic surfaces in CP5. Under this characterization, we construct eight families of conformal minimal surfaces in HP2. Then, we study horizontal Veronese sequences in CP4 and CP5, and we transform the construction into solving a quadratic equation. Based on this, we get some examples of conformal minimal two-spheres in HP2 with constant curvature 45 and 413.
KW - Conformal minimal surface
KW - Quaternionic projective space
KW - Twistor map
UR - http://www.scopus.com/inward/record.url?scp=85015661028&partnerID=8YFLogxK
U2 - 10.1007/s10231-017-0653-4
DO - 10.1007/s10231-017-0653-4
M3 - Article
AN - SCOPUS:85015661028
SN - 0373-3114
VL - 196
SP - 2063
EP - 2076
JO - Annali di Matematica Pura ed Applicata
JF - Annali di Matematica Pura ed Applicata
IS - 6
ER -