* U.S. yield curve flattens after steepening the last few sessions * U.S. consumer prices unchanged in October * U.S. 30-year bond auction shows solid results (Adds new comment, U.S. 30-year auction outcome, updates prices) By Gertrude Chavez-Dreyfuss NEW YORK, Nov 12 (Reuters) - U.S. Treasury yields sank on Thursday, weighed down by the persistent rise in coronavirus cases around the world and data showing inflation remained benign in the world"s largest economy. The U.S. yield curve, viewed in part as a gauge of risk appetite, also flattened on Thursday, after steepening the last few sessions on positive COVID-19 vaccine news from Pfizer Inc early this week. Analysts said investors are realizing that distributing the vaccine to the world would take time. Demand at the $27 billion U.S. 30-year bond auction on Thursday was decent, analysts said, although the yield of 1.68% exceeded market expectations at the bid deadline. The bid-to-cover ratio was 2.29, slightly higher than the August refunding but the same number as the October reopening. Indirect bidders, which include foreign central banks, took 61.9% of the total, a little better than the 59.8% takedown at the August refunding. "The 30-year auction was solid," said Jim Vogel, senior rates strategist, at FHN Financial in Memphis. "We had good participation in the face of a 9 basis-point rally in the 30-year and therefore we have kept the price gains in Treasuries today." Thursday"s data on U.S. consumer prices, which were unexpectedly unchanged in October, kept yields lower. Excluding the volatile food and energy components, CPI was also flat after rising 0.2% the prior month. In afternoon trading, U.S. benchmark 10-year yields were down at 0.884%, from 0.989% late on Tuesday. Bond markets were closed on Wednesday for Veterans Day. Stan Shipley, fixed income strategist at Evercore ISI in New York, said the 1% yield on the 10-year note is a big psychological level. "But it"s going to take a little bit of effort to get through that 1%, and today"s CPI number didn"t help. Rising coronavirus cases every day won"t help either," he added. On Thursday, the U.S. Centers for Disease Control and Prevention (CDC) reported 10,314,254 cases, up 143,408 from its previous count, and said the number of deaths had risen by 1,479 to 241,069. U.S. 30-year yields fell to 1.645% from Tuesday"s 1.76%. On the front end of the curve, U.S. two-year yields slipped to 0.176% from 0.185% on Tuesday. The U.S. yield curve, meanwhile, flattened, with the spread between the two-year and 10-year narrowing to 70 basis points . U.S. President-elect Joe Biden moved ahead with planning his new administration on Thursday as his fellow Democrats in Congress blasted Republican "shenanigans" challenging Donald Trump"s election loss. The post-election uncertainty has weighed on bond investors as well and kept a lid on U.S. rates. In Thursday"s research note about the U.S. election outcome, Fitch Ratings said it expected a "noisy but ultimately orderly" shift of power to the Biden administration. The ratings agency said it also expected Republicans to keep control of the U.S. Senate, noting that a divided government could pose a "serious obstacle to legislation that would address structural issues." November 12 Thursday 3:25PM New York / 2025 GMT Price Current Net Yield % Change (bps) Three-month bills 0.09 0.0913 -0.005 Six-month bills 0.1 0.1014 -0.003 Two-year note 99-230/256 0.1768 -0.008 Three-year note 100-14/256 0.2317 -0.026 Five-year note 99-72/256 0.3964 -0.064 Seven-year note 99-16/256 0.6378 -0.088 10-year note 99-240/256 0.8815 -0.108 20-year bond 95-12/256 1.4132 -0.118 30-year bond 93-172/256 1.6448 -0.115 DOLLAR SWAP SPREADS Last (bps) Net Change (bps) U.S. 2-year dollar swap 8.25 0.50 spread U.S. 3-year dollar swap 7.25 1.25 spread U.S. 5-year dollar swap 5.50 0.50 spread U.S. 10-year dollar swap -1.00 -1.75 spread U.S. 30-year dollar swap -34.50 0.00 spread (Reporting by Gertrude Chavez-Dreyfuss; Additional reporting by Ross Kerber in Boston; Editing by Chizu Nomiyama, Jonathan Oatis