Knowledge (XXG)

Wente torus

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58: 176: 85: 119: 25: 17: 34: 97: 128: 142: 138: 77: 110: 65: 61: 170: 81: 114: 148: 161: 73: 133: 93: 89: 151:, University of Toledo Mathematics Department, retrieved 2013-09-01. 28: 96:). There are similar examples known for every positive 37: 52: 72:). It is a counterexample to the conjecture of 8: 115:"Counterexample to a conjecture of H. Hopf." 132: 44: 40: 39: 36: 92:(though this is true if the surface is 69: 7: 14: 177:Differential geometry of surfaces 162:Visualization of the Wente torus 53:{\displaystyle \mathbb {R} ^{3}} 86:constant-mean-curvature surface 120:Pacific Journal of Mathematics 1: 193: 134:10.2140/pjm.1986.121.193 54: 55: 18:differential geometry 35: 66:Henry C. Wente 50: 184: 145: 136: 64:, discovered by 59: 57: 56: 51: 49: 48: 43: 192: 191: 187: 186: 185: 183: 182: 181: 167: 166: 158: 149:The Wente torus 111:Wente, Henry C. 109: 106: 38: 33: 32: 12: 11: 5: 190: 188: 180: 179: 169: 168: 165: 164: 157: 156:External links 154: 153: 152: 146: 105: 102: 62:mean curvature 47: 42: 13: 10: 9: 6: 4: 3: 2: 189: 178: 175: 174: 172: 163: 160: 159: 155: 150: 147: 144: 140: 135: 130: 126: 122: 121: 116: 112: 108: 107: 103: 101: 99: 95: 91: 87: 83: 79: 75: 71: 67: 63: 45: 30: 27: 23: 19: 124: 118: 60:of constant 21: 15: 127:: 193–243, 76:that every 22:Wente torus 104:References 74:Heinz Hopf 171:Category 113:(1986), 94:embedded 26:immersed 143:0815044 82:compact 68: ( 141:  90:sphere 78:closed 24:is an 98:genus 88:is a 29:torus 70:1986 20:, a 129:doi 125:121 31:in 16:In 173:: 139:MR 137:, 123:, 117:, 100:. 84:, 80:, 131:: 46:3 41:R

Index

differential geometry
immersed
torus
mean curvature
Henry C. Wente
1986
Heinz Hopf
closed
compact
constant-mean-curvature surface
sphere
embedded
genus
Wente, Henry C.
"Counterexample to a conjecture of H. Hopf."
Pacific Journal of Mathematics
doi
10.2140/pjm.1986.121.193
MR
0815044
The Wente torus
Visualization of the Wente torus
Category
Differential geometry of surfaces

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